Answer:
r=2q-6
Step-by-step explanation:
10q-5r=30
Subtract 10q from both sides:
-5r=30-10q
Divide both sides by -5:
r=2q-6
Hope this helps!
As quality control manager at a raisin manufacturing and packaging plant, you want to ensure that all the boxes of raisins you sell are comparable, with 30 raisins in each box (assume the population average number of raisins per box is 30). In the plant, raisins are poured into boxes until the box reaches its sale weight. To determine whether a similar number of raisins are poured into each box, you randomly sample 36 boxes about to leave the plant and count the number of raisins in each. In this sample, you find the mean number of raisins in each box to be 28.05, with a standard deviation of 3.87.
1. Perform a two-tailed, single sample t test (p<.05) to determine whether the average number of raisins per box differs from the expected 30.
2. What type of statistical analysis should be run to address this question?3. What are the assumptions of your chosen statistical test?4. Identify the null and alternative/research hypotheses in both words and symbols.
Answer:
Step-by-step explanation:
The population average number of raisins per box is 30.
The type of statistical analysis to be run here is the inferential statistical analysis and its assumptions include normality, linearity and equality of variance.
Null hypothesis: Average number of raisins per box is 30: u = 30
Alternative hypothesis: Average number of raisins per box is not 30: u ≠ 30
To perform a two tailed single sample test, we have
z statistic = (the sample mean - hypothesized mean) / (SD/√n)
sample mean = 28.05, SD = 3.87 hypothesized mean = 30 n = 36
Thus, we have 28.05 - 30 / (3.87/√36)
= -1.95 / (3.87/6)
= -1.95 / 0.645
= -3.023
we say this is a left tailed test and use the negative z table
where -3.02 = 0.0013
To determine whether the average number of raisins per box differs from the expected 30.
Using p < 0.05, since the observed value 0.0013 is less than 0.05, we conclude the the average number of raisins per box differs from the expected 30.
What is the side length of a square with an area of 95
Answer:
23.75
Step-by-step explanation:
95/4
23.75
Answer:
A≈9.75
Step-by-step explanation:
The side length can be found by getting the square root of 95.
Since all sides are the same on a square, this means that 9.75² gives us 95, which it does.
Hope this helps!
-MoCKEry
please help :( please help :( please help :( please help :( please help :( please help :( please help :( please help :(
Answer:
(1) 23.55mm³
(2) 340.17in³
Step-by-step explanation:
Volume of a cone is: [tex]V=\frac{1}{3} \pi r^2h[/tex]
'r' - radius
'h' - height
Cone 1:The height of Cone 1 is 10 mm. The Diameter of Cone 1 is 3mm.
Radius is half the Diameter.
[tex]3/2=1.5[/tex]
The radius is 1.5 mm.
[tex]\text {Using 3.14 as pi: }\\V=(1/3)3.14*1.5^2*10\\V=(1/3)3.14*2.25*10\\V=(1/3)70.65\\\boxed{V=23.55}[/tex]
The volume of Cone 1 should be about 23.55mm³.
Cone 2:The height of Cone 2 is 13 in. The Radius of Cone 2 is 5 in.
Using 3.14 as pi:
[tex]V=(1/3)3.14*5^2*13\\V=(1/3)3.14*25*13\\V=(1/3)1020.5\\\boxed {V=340.166666667}[/tex]
340.166666667 ≈ 340.17
The volume of Cone 2 should be about 340.17in³.
Point A is located at 11 on the number line. Point B is 5 less than Point A, where on the number line is Point B
Answer:
point B is located at 6 on the number line
Step-by-step explanation:
u subtract 5 from 11
Mike took clothes to the cleaners three times last month. First, he brought 4 shirts and 1 pair of slacks and paid $15.95. Then he brought 7 shirts, 4 pairs of slacks, and 1 sports coat and paid $49.38. Finally, he brought 3 shirts and 1 sports coat and paid $15.46. How much was he charged for each shirt, each pair of slacks, and each sports coat? Mike was charged $ nothing for each shirt, $ nothing for each pair of slacks, and $ nothing for each sports coat.
Answer:
Each Shirt ≈ $2.49
Each Pair of Slacks ≈ $5.99
Each Sports Coat ≈ $7.99
Step-by-step explanation:
Mike took clothes to the cleaners three times last month.
Let S denotes shirts, P denotes pair of slacks and C denotes sports coat.
First, he brought 4 shirts and 1 pair of slacks and paid $15.95.
Mathematically,
4S + P = 15.95 eq. 1
Then he brought 7 shirts, 4 pairs of slacks, and 1 sports coat and paid $49.38.
Mathematically,
7S + 4P + C = 49.38 eq. 2
Finally, he brought 3 shirts and 1 sports coat and paid $15.46.
Mathematically,
3S + C = 15.46 eq. 3
We are asked to find how much was he was charged for each shirt, each pair of slacks, and each sports coat.
4S + P + 0C = 15.95 eq. 1
7S + 4P + C = 49.38 eq. 2
3S + 0P + C = 15.46 eq. 3
We have 3 equations and 3 unknowns, they can be solved simultaneously using calculator or using online system of equations solver.
Using online system of equations solver yields,
S ≈ $2.49
P ≈ $5.99
C ≈ $7.99
So that means Mike was charge $2.49 for each shirt, $5.99 for each pair of slacks and $7.99 for each sports coat.
For the given functions, (a) express dw/dt as a function of t, both by using the chain rule and by expressing w in terms of t and differentiating directly with respect to to Then (b) evaluate dw/dt at the given value of t. w = 7y e^x - Inz,x = ln(t^2 + 1), y = tan^-1t,z=e^t;t = 1
(a) dw/dt =?
By the chain rule,
[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}[/tex]
We have
[tex]w=7ye^x-\ln z\implies\begin{cases}\dfrac{\partial w}{\partial x}=7ye^x\\\\\dfrac{\partial w}{\partial y}=7e^x\\\\\dfrac{\partial w}{\partial z}=-\dfrac1z\end{cases}[/tex]
and
[tex]\begin{cases}x=\ln(t^2+1)\\y=\tan^{-1}t\\z=e^t\end{cases}\implies\begin{cases}\dfrac{\mathrm dx}{\mathrm dt}=\dfrac{2t}{t^2+1}\\\\\dfrac{\mathrm dy}{\mathrm dt}=\dfrac1{t^2+1}\\\\\dfrac{\mathrm dz}{\mathrm dt}=e^t\end{cases}[/tex]
Putting everything together, we get
[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{14ye^xt}{t^2+1}+\dfrac{7e^x}{t^2+1}-\dfrac{e^t}z[/tex]
[tex]x=\ln(t^2+1)[/tex], so [tex]e^x=e^{\ln(t^2+1)}=t^2+1[/tex], and [tex]z=e^t[/tex], so [tex]\frac{e^t}z=1[/tex].
[tex]\dfrac{\mathrm dw}{\mathrm dt}=14yt+7-1[/tex]
[tex]\dfrac{\mathrm dw}{\mathrm dt}=14t\tan^{-1}t+6[/tex]
Then when [tex]t=1[/tex], the derivative has a value of [tex]\frac{7\pi}2+6[/tex].
Which inequality is true if p=3.4
3p<10.2
13.6<3.9p
5p>17.1
8.5>2.5
Answer:
None of the inequalities are correct if p = 3.4
Step-by-step explanation:
Mathematical inequality is an order relation proposition existing between two algebraic expressions connected through the signs: unequal than ≠, greater than>, less than <, less than or equal to ≤, as well as greater than or equal to ≥, resulting in both expressions of different values. That is, an inequality is a relationship that exists between two quantities or expressions and, which indicates that they have different values.
To check an inequality, you must replace the inequality variable with the value of the solution. In this case, being p=3.4, you must do it with each of the inequalities, as shown below:
A. 3p<10.2 ⇒ 3*3.4<10.2 ⇒ 10.2 <10.2
This inequality is not true, because 10.2 is not less than 10.2, but they are equal.
B. 13.6<3.9p ⇒ 13.6<3.9*3.4 ⇒ 13.6<13.26
This inequality is not true, because 13.6 is greater than 13.26 and not less as the inequality shows.
C. 5p>17.1 ⇒ 5*3.4 >17.1 ⇒ 17 > 17.1
This inequality is not true, because 17 is less than 17.1 and not greater as the inequality shows.
D. 8.5> 2.5p ⇒ 8.5 >2.5*3.4 ⇒ 8.5 > 8.5
This inequality is not true, because 8.5 is not less than 8.5. These values are the same.
None of the inequalities are correct if p = 3.4
The correct answer is C. By substituting the greatest number in each set for p, you can quickly tell which sets make the inequality false.
What is the solution to the equation?
t+55=466
t+55
Answer:
t=411
Step-by-step explanation:
t+55=466
466-55
Subtract the numbers
t=411
The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold StartFraction one-third EndFraction of the short-sleeved shirts and StartFraction one-half EndFraction of the long-sleeved shirts, for a total of 100 shirts. How many short-sleeved shirts were ordered?
How many long-sleeved shirts were ordered?
Answer:
150 short-sleeved shirts100 long-sleeved shirtsStep-by-step explanation:
Let S and L represent the numbers of short- and long-sleeved shirts ordered.
The expected earnings were ...
5S +10L = 1750
The number sold was ...
(1/3)S + (1/2)L = 100
We can multiply the first equation by 1/5 and the second equation by 6 to put the equations into standard form:
S +2L = 3502S +3L = 600Subtracting the second equation from twice the first gives ...
2(S +2L) -(2S +3L) = 2(350) -(600)
L = 100 . . . . . . simplify
2S +3(100) = 600
S = 150
150 short-sleeved and 100 long-sleeved shirts were ordered.
Answer:
b
Step-by-step explanation:
i did it on edge
At the bank, Mr Smith changes a £5 note for 20p pieces.
How many 20p pieces does he-get?
Answer:
erm
Step-by-step explanation:
25
raine divides three 2-ounce bags of rice into smaller bags. The first bag is divided into bags weighing 1/6-ounce each, and the third bag is divided into bags weighing 1/2- ounce each.
Answer:
There would be
- 12 bags of 1/6-ounce rice.
- 6 bags of 1/3-ounce of rice.
- 4 bags of 1/2-ounce of rice.
-The line plot is presented in the attached image to this answer.
1) There are 22 bags that weigh at least 1/6 of an ounce.
2) There are 4 bags that weigh more than 1/3 of an ounce.
3) The combined total of the 1/2-ounce bags = 2 ounces.
4) The average weight of the bags = (3/11) of an ounce.
Step-by-step explanation:
Complete Question
Raine divides three 2-ounce bags of rice into smaller bags. The first bag is divided into bags weighing 1/6-ounce each, the second bag is divided into bags weighing 1/3-ounce each and the third bag is divided into bags weighing 1/2- ounce each. Find the number of 1/6, 1/3 and 1/2 bags and graph it in a line plot.
1) How many bags weigh at least 1/6 of an ounce?
2) How many bags are more than 1/3 of an ounce?
3) What is the combined total of the 1/2 ounce bags?
4) What is the average weight of each of the bags?
Solution
Let the number of 1/6-ounce, 1/3-ounce and 1/2-ounce bags be x, y and z respectively.
(1/6) × x = 2
x = 2 × 6 = 12 bags of 1/6-ounce rice.
(1/3) × y = 2
y = 2 × 3 = 6 bags of 1/3 ounce of rice.
(1/2) × z = 2
z = 2 × 2 = 4 bags of 1/2-ounce rice.
The line plot is presented in the attached image to this answer.
1) All of the bags weigh at least 1/6 of an ounce. Hence, the number of bags that weigh more than 1/6 of an ounce = 12 + 6 + 4 = 22 bags
2) The bags that weigh more than 1/3 of an ounce are the 1/2-ounce bags, and there are only 4 of them. Hence, 4 bags weigh more than 1/3 of an ounce.
3) Combined total of the 1/2 ounce bags
= 4 bags × (1/2-ounce per bag) = 2 ounces.
4) The average weight of the bags is given as the sum total of the weight of the bags divided by the number of bags.
Total weight of the bags = [12 × (1/6)] + [6 × (1/3)] + [4 × (1/2)] = 2 + 2 + 2 = 6 ounces.
Total Number of bags = 12 + 6 + 4 = 22 bags
Average weight of the bags = (6/22) = (3/11) ounce per bag.
Hope this Helps!!!
Paj is filling a 9-cubic-inch flower pot with soil from small bags. Each bag of soil contains 2 2/3
cubic inches of soil. Exactly how many bags of soil are needed for Paj to fill the flower pot?
Answer:
3.375 bags of soil are needed for Paj to fill the flower pot
Step-by-step explanation:
This question can be solved using a rule of three.
One bag contains 2 + (2/3) = (8/3) cubic inches of soil. How many bags are needed to fill 9 cubic inches of soil?
1 bag - (8/3) cubic inches
x bags - 9 cubic inches
[tex]\frac{8x}{3} = 9[/tex]
[tex]8x = 27[/tex]
[tex]x = \frac{27}{8}[/tex]
[tex]x = 3.375[/tex]
3.375 bags of soil are needed for Paj to fill the flower pot
Paj needs 3.375 bags of soil to fill the bag.
Each bag contains 2²/₃ inch³ of soil and they need to fill up a 9 inch³ pot of soil.
First convert the mixed fraction to an improper one:
2²/₃ = 8/3
The number of bags needed is:
= Volume of pot / Quantity of soil in each bag
= 9 ÷ 8/3
= 9 x 3/8
= 3.375 bags of soil
Paj therefore needs 3.375 bags of soil to fill the pot
Find out more at https://brainly.com/question/17205287.
The ratio of Mark’s age to Reeta’s age is 3 : 5 Mark’s age is 24 years. Work out Reeta's age.
The ratio of Reeta's age and Site's age is 3:5 and the sum of their ages is 80 years. The ratio of their ages after 10 years will be
William and Stephanie are painting the bedrooms in their house. If he had to paint the bedrooms himself, it would take William four hours to complete the job. If Stephanie alone were to paint the bedrooms, it would take her six hours.
Working together, how long will it take William and Stephanie to paint the bedrooms?
William can do 1/4 of the job every hour by himself.
Stephanie can do 1/6 of the job every hour by herself.
If they don't distract each other while working together, they can do (1/4 + 1/6) of the job every hour.
That's (3/12 + 2/12) = 5/12 job per hour working together.
The complete job will take them (12/5) hour .
That's 2-2/5 hours, or 2 hours 24 minutes.
They both can do the painting in 2hours 24 minutes by solving the fraction.
What is a fraction?
It is a combination of numerator and denominator. It is always in decimal
if solved properly.
How to calculate time?William can do 1/4 of the job every hour himself. Stephanie can do 1/6 of the job every hour herself, they can do (1/4 + 1/6) of the job every hour.
That's (3/12 + 2/12) = 5/12 job per hour working together.
The complete job will take them (12/5) hour .
or 2 hours 24 minutes.
Learn more about fraction at https://brainly.com/question/78672
#SPJ2
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answer:
A
Step-by-step explanation:
The form for a parabola with vertex form is y=(x-h)^2+k, where h is the x coordinate and k is the y. Therefore, since the x coordinate of the graph is -2, the answer is A. Hope this helps!
Answer:
its A
hop this helps
Job has to pay $9.00 admission for the skating rink and $2 per to rent rollerblades how many hours can he skate for $19
Answer:
5 hours
Step-by-step explanation:
Here we can create an equation to solve for the number of hours (x) this man can skate for.
Since he has to pay a $9 flat fee, that will be a constant value or our y-intercept in this case.
Our equation will be y = 2x + 9
Since we know his budget is $19, we can set our equation equal to 19, or replace y in this case.
So now we have 19 = 2x +9
Now we need to subtract 9 from both sides to get 10 = 2x
Then we need to divide both sides by 2 to get 5 = x
So this man can skate for 5 hours considering his budget
John borrowed $150,500 to start up his business. He borrowed the money at a 7.75% simple
interest rate for 2 years. How much does John have to pay back at the end of two years
Answer:
John have to pay back $23,327.50 at the end of two years
Step-by-step explanation:
Simple Interest (I) = (PRT) ÷ 100
where P = Principal, R = Rate, T= Time
I = ($150500 × 7.75 × 2) ÷ 100
I = ($2332750) ÷ 100
I = $23,327.50
Please answer this correctly without making mistakes
Answer:
g=56
Step-by-step explanation:
In similar shapes, corresponding sides are always in the same ratio.
For example,
if the sides in triangle 1 were a and b, and triangle 2 had side lengths c and d, c and a had the same ratios, and b and d had the same ratios
and triangle 1 was similar to triangle 2, the ratio between the sides of the triangles would be
a/c, which is also equal to b/d
What that means is that in this situation, 8/5=g/35.
8/5=g/35
Cross multiply.
(8)*(35)=g*(5)
280=5g
g=56
And object Weighs a quarter of a kilogram . I add one half of a kilogram to the object. I take 200g off. I double the mass of the object. I add one tone the object and then half it what is the mass of object
If the final weight is halved then the mass of the object will be 500,550 grams
Measurement of an object1 kg of an object = 1000 grams
If an object weighs a quarter of a kilogram, then
New weight = 1/4(1000) = 250 grams
If I add one-half of a kilogram to the object, then the new weight will be 750grams
If I take 200grams off, the new weight will be 550 gramsIf the mass is doubled, then the new weight will be 2(550) which is 1100gramsIf 1 tonne is added, then the new mass will be 1000000 + 1100)grams.If the final weight is halved then the mass of the object will be 500,550 grams
Learn more on measurement here: https://brainly.com/question/13893070
Which game isn’t fair for two players to play?
Answer:
cube game
Step-by-step explanation:
one of them wins every time
A number cube is rolled. Player 1 gets a point for any number that is 3 or higher, and player 2 gets a point for any number less than 3
If a number cube is rolled and Player 1 gets a point for any number that is 3 or higher and Player 2 gets a point for any number less than 3 it wouldn't be fair to Player 2 because Player 1 has a higher chance of getting points because he/she has more opportunities.
I hope this is correct
Which equations has -6minus as a possible value of a?
Answer:
Perimetrul triunghiului ABC este egam cu 36 cm, iar AB = 15 cm si AC = 13 cm. Lungimea segmentului BC = cu...
Step-by-step explanation:
Adding 5+8+2 can be accomplished by
Answer:
8+5=13
13+2=15
your answer is 15
You have to add : )
Step-by-step explanation:
Hope this helps : )
Pythagorean Theorem Word
Problems
You start driving north for 32 miles, turn
right, and drive east for another 24 miles,
At the end of driving, what is your straight
line distance from your starting point?
Answer:
40 miles
Step-by-step explanation:
In the attached diagram, Point A is the starting point and C is the end point. We want to determine the distance from A to C.
The path driven forms a right triangle in which AC is the hypotenuse.
We therefore use the Pythagorean Theorem to solve for the AC.
Pythagorean Theorem: [tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
[tex]|AC|^2=32^2+24^2\\|AC|^2=1600\\|AC|=\sqrt{1600}\\ |AC|=40$ miles[/tex]
The straight line distance from the starting point is 40 miles.
An importer of electronic goods is considering packaging a new, easy-to-read instruction booklet with DVD players. It wants to package this booklet only if it helps customers more than the current booklet. Previous tests found that only 30% of customers were able to program their DVD player. An experiment with the new booklet found that 16 out of 60 customers were able to program their DVD player. a. State the null and the alternative hypot
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
What’s the correct answer for this?
Answer:
Step-by-step explanation:
52units
Answer:
A
Step-by-step explanation:
In the attached file
Write what the expressions below best represent within the context of the word problem.
Mark had 3 times as many quarters as nickels. He had $1.60 in all. How many nickels and how many quarters did Mark
have?
x represents
3x represents
TURN IT IN
NEXT QUESTION
ASK FOR HELP
Answer:
2 nickels
6 quarters
Step-by-step explanation:
Let quarters be 3x and nickels be $x
if Mark had 3 times as many quarters as nickels, and if he had $1.60 in all, than
( 0.25)3x + 0.05x=1.6
0.75x+ 0.05x=1.6
0.8x=1.6
x=1.6/0.8
x=2 nickels
and 3 (2)=6 quarters
Answer:
There are 4 quarters and 12 nickels.
Step-by-step explanation:
A quarter is equal to $0.25.
A nickel is equal to $0.05.
Let the number of nickels be y.
Let the number of quarters be x.
Mark had 3 times as many quarters as nickels. This means that:
y = 3x
3x represents the number of nickels.
We are told that he had $1.60 in all. This means that:
0.25x + 0.05y = 1.60
=> 0.25x + 0.05 * 3x = 1.60
0.25x + 0.15x = 1.60
0.40x = 1.60
=> x = 1.6 / 0.4 = 4
Therefore:
y = 3 * 4 = 12
There are 4 quarters and 12 nickels.
PLEASEEEE HELPP MEEE WITHHH NUMBERSSS 9 AND 10
PLEASEEE HELPPP MEEEEE!!!!!!!!
Answer:
9: 89°
Step-by-step explanation:
Inside of a triangle is 180, so 180-39-52=89
I'm sorry I can't answer 10 for you
In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 329 trials, the touch therapists were correct 154 times.
a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?
b. Using Emily's sample results, what is the best point estimate of the therapists' success rate?
c. Using Emilys sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.
Answer:
a) [tex] p = 0.5[/tex]
b) [tex] \hat p= \frac{X}{n}= \frac{154}{329}= 0.468[/tex]
c) [tex]0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423[/tex]
[tex]0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513[/tex]
And the 90% confidence interval for the true proportion is given by (0.527;0.593).
Step-by-step explanation:
Part a
For this case we don't have any prior info given so then the probability assumed for this case is:
[tex] p = 0.5[/tex]
Part b
For this case the proportion of success is given by:
[tex] \hat p= \frac{X}{n}= \frac{154}{329}= 0.468[/tex]
Part c
The confidence interval for the true proportion would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 90% confidence interval the value of and , and the critical value would be given by:
[tex]z_{\alpha/2}=1.64[/tex]
The confidence interval is given by:
[tex]0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423[/tex]
[tex]0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513[/tex]
And the 90% confidence interval for the true proportion is given by (0.527;0.593).
An estimated 3 out of every 25 men are left-handed.
What percent of men are left-handed?
%
Answer:
12 %
Step-by-step explanation:
The fraction of men that are left handed is 3/25
Percent means out of 100, so get the fraction with a denominator of 100
3/25 *4/4 = 12/100
12 %
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 10% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 10% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 13 customers buy a magazine?
Answer:
0.55% probability that exactly 5 out of the first 13 customers buy a magazine
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of other customers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
10% of his customers buy a magazine
This means that [tex]P = 0.1[/tex]
What is the probability that exactly 5 out of the first 13 customers buy a magazine?
This is P(X = 5) when n = 13. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{13,5}.(0.1)^{5}.(0.9)^{8} = 0.0055[/tex]
0.55% probability that exactly 5 out of the first 13 customers buy a magazine
Answer:
[tex] P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554[/tex]
So then he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554
Step-by-step explanation:
Let X the random variable of interest "number of customers that buy a magazine", on this case we can model the variable of interest with this distribution:
[tex]X \sim Binom(n=13, p=0.1)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find this probability:
[tex] P(X=5)[/tex]
And using the probability mass function we got:
[tex] P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554[/tex]
So then he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554