Answer:
(a) The probability distribution of the random variable X is Binomial.
(b) The mean and standard deviation of the 25-question test are 5 and 2 respectively.
(c) The value of x is 0.34.
Step-by-step explanation:
The random variable X is defined as the number of correct answers given by a person who is guessing each answer on a 25-question exam.
There are five possible answer for every question.
This implies that the probability of getting a correct answer is:
P (X) = 0.20.
There are a total of n = 25 questions.
Every answer is independent of the others.
(a)
The random variable X has finite number of independent trials (i.e. 25 questions). There are only two outcomes for each trial, i.e. Success = correct answer and Failure = wrong answer. Each trial has the same probability of success (, i.e. P (X) = 0.25).
Thus, the probability distribution of the random variable X is Binomial with parameters n = 25 and p = 0.20.
(b)
Compute the mean of the random variable X as follows:
[tex]E(X)=np\\=25\times 0.20\\=5[/tex]
Compute the standard deviation of the random variable X as follows:
[tex]SD(X)=\sqrt{np(1-p)}\\=\sqrt{25\times 0.20\times (1-0.20)}\\=2[/tex]
Thus, the mean and standard deviation of the 25-question test are 5 and 2 respectively.
(c)
The sample is large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
1. np ≥ 5
2. n(1 - p) ≥ 5
Check the conditions as follows:
[tex]np=25\times 0.20=5=5\\\\n(1-p)=25\times (1-0.20)=20>5[/tex]
Thus, a Normal approximation to binomial can be applied.
So, [tex]X\sim N(5, 2^{2})[/tex]
It is provided that the minimum passing score foe the test is such that only 1% of students who are guessing will pass the test.
That is P (X < x) = 0.01.
⇒ P (Z < z) = 0.01
The value of z is -2.33.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-2.33=\frac{x-5}{2}\\\\x=5-(2.33\times 2)\\\\x=0.34[/tex]
Thus, the value of x is 0.34.
What is the approximate distance from one corner of the soccer field to the opposite corner? 60 yards, 100 yards. A: 160 yards B: 130 yards C: 126 yards D: 177 yards
Answer:
117 yards
Step-by-step explanation:
A field is in the shape of a rectangle
The distance from one corner of the field to the opposite corner represent the diagonal of a rectangle
The diagonal of a rectangle is calculated using
D^2= l^2 + w^2
Where,
D=diagonal
L=length=100 yards
W=width=60 yards
D^2= l^2 + w^2
=100^2+60^2
=10,000+3,600
=13,600
D^2=13,600
D=√13,600
=116.62 yards
Approximately
117 yards
Answer:
177 yeard d
Step-by-step explanation:
the approximate distance is 177 yeard
The Scale on a map shows that 200 is represented by 5 inches on a map .Which proportion can be used to find the distance on the map x, that represents 50 miles? A.) 5/200 = X/50 B.)200/5 = X/50 C.) 50/200 = 5/X D.)5/50 = X/200
Answer:
a
Step-by-step explanation:
just keep the miles on bottom and the inches on top
Find the surface area of the pyramid. The side lengths of the base are equal.
17 cm
12 cm
These are
square centimeters.
Answer:
The answer is 204 square cm.
Step-by-step explanation:
You are asking for the surface area, and while calculating the surface area you will multiply the quantities.
Surface Areas: 17 cm multiply 12 cm
17 X 12 = 204
The answer is 204 sq. cm
Answer:
204
Step-by-step explanation:
plz Help your fav. Marshmello i wasn' t,,,,, xx born yesterday.
Answer:
[tex] \boxed{D. \: x = 5} [/tex]
Step-by-step explanation:
[tex] = > 1 - 2x - 1 = - 10 \\ \\ = > 1 - 1 - 2x = - 10 \\ \\ = > 0 - 2x = - 10 \\ \\ = > \cancel{ - }2x = \cancel{ - }10 \\ \\ = > 2x = 10 \\ \\ = > x = \frac{10}{2} \\ \\ = > x = 5[/tex]
Answer:
the answer is attached to the picture
The following options are available for a car wash
Standard wash £8
Deluxe wash £12
In one day 60 customers have their car washed. The ratio of customers choosing the standard car wash to those choosing the deluxe car wash is 3:2
What is the total takings at the car wash for the day?
Answer:
£576
(would really, reallly appreciate the brainliest)
Step-by-step explanation:
8 * 60 * 3/5 + 12 * 60 * 2/5
Identify the sequence as arithmetic, geometric, or neither. Justify your answer by trying to describe the pattern (how are they moving from one number to the next).
1, 1, 2, 6, 24, 120,...
Answer:
factorials
Step-by-step explanation:
0!=1,1!=1,2!=2,3!=6,4!=24,5!=120,6!=720,...
sequence is n! starting at 0
£20 is divided between Caroline, Sarah & Gavyn so that Caroline gets twice as much as Sarah, and Sarah gets three times as much as Gavyn. How much does Caroline get?
Answer:
Caroline gets £12
Step-by-step explanation:
Let Caroline share be x
Let Sarah share be y
Let gavyn share be z
X = 2y
Y = 3z
X+ y + z = 20
X = 6z
Y = 3z
6z + 3z +z = 20
10z= 20
Z= 2
Y = 3z
Y= 3*2
Y= 6
X= 6z
X= 6*2
X= 12
Caroline gets £12
Sara and Don are considering a $130,000 mortgage for 30 years at 4.8% paid monthly. What is their monthly payment. If they pay the minimum each month what is their total payback of this loan and how much interest will they pay.
Answer:Monthly payment is $682.06
Step-by-step explanation:
Answer:
The formula to calculate the final cost:
C = 130000 x (1 + (4.8/100)/12)^(30 x 12) = 547116.69
Minimum payment each month:
M = 547116.69/(30 x 12) = 1519.77
Interest they have to pay: 547116.69 - 130000 = 417116.69 dollar
Hope this helps!
:)
PLS HELP ASAP twenty points Find the value of c such that the expression is a perfect square trinomial.
x^2-14x+c
Answer:
49
Step-by-step explanation:
x^2-14x+c
Take the coefficient of x
-14
Divide by 2
-14/2 = -7
Square it
(-7)^2
49
This is the number you add
a mini dvd has a radius of 4 centimeters. there is a hole in the middle of the mini dvd with a radius of 1 centimeter. what is the area of one side of the mini dvd
Answer:
Area of one side of mini DVD = 15π or 47.12 cm²
Step-by-step explanation:
The radius of the mini DVD is;r = 4cm.
Area of a circle = πr²
Thus, Area of mini DVD = π × 4² = 16π
Now,we are told the mini DVD has a hole with a radius of 1 cm.
Area of hole = π × 1² = π
To find the area of one side of the mini DVD, we have to subtract the area of the hole from the area of the DVD.
Thus;
Area of one side of mini DVD = 16π - π
= 15π = 47.12 cm²
what is the mean of :20 20 20 22 22 24 26 26 26
The mean of a set of numbers is the sum divided by the number of terms.
Answer: 22.9
Answer:
YOU ADD AND DIVIDE FOR THE MEAN
Step-by-step explanation:
add 20 + 20 + 20 + 22 + 22 + 24 + 26 + 26 + 26 equaling to = 206
divide by 9 equaling to = 22.88
PLEASE ANSWER ASAP! WILL GIVE ~BRAINLIEST~ ANSWER (IF CORRECT)
Rewrite the expression in the form 9^n
9^7/9^5
Answer:
a^b/a^c = a^b-c
9^7/9^5=9^7-5
=9^2 ( ANSWER )
Step-by-step explanation:
please mark me BRAINLIEST
mary had 1 3/4 pound of blackberries. Mary's friend ate 3/4 of the blackberries. How many pounds of blackberries did Mary friend eat?
Answer:
Shown in the explanation below,
Step-by-step explanation
Mary had 1 3/4 pounds
Mary friend eat 3/4 blackberry which is
3/4. × 7/4 = 21/ 16 = 1 5/16
to find the average of a set of numbers, add up all the items and divide by?
Answer:
you add up all of the items and then divide by the total number of items.
Step-by-step explanation:
For example,
Total/Number of Items = Average
Set: 1,6,4,5
(1+6+4+5)/4
16/4 = 4
4 is the average of the items above.
Good luck!!
Rearrange the equation so u is the independent variable.
4u+8w=-3u+2w
w= __
Rearrange the equation so m is the independent variable.
-2m - 5n = 7m - 3n
Answer:
w = 7u/6
u = 6w/7
m = 2n/-9
n = -9m/2
Step-by-step explanation:
4u + 8w = -3u + 2w
4u - 4u +8w = -3u - 4u +2w
8w -2w = -7u + 2w - 2w
6w = -7u
w = 7u/6
u = 6w/7
AND
-2m - 5n = 7m - 3n
-2m -7m -5n = 7m -7m -3n
-9m -5n +5n = -3n +5n
-9m = 2n
m = 2n/-9
n = -9m/2
Which expression is equivalent to (sf)(6)
Answer:
(st)(6)= s(6) * t(6)
Step-by-step explanation:
(st)(6)
(st)(x)= s(x) * t(x) we multiply it
(st)(6)= s(6) * t(6)
Hope this helps.
A bakery sold 100 mocha cupcakes in a day, which was 20% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
500
Step-by-step explanation:
percentage is the quantitative way to express number of things out of 100 things.
For example : 20% of bananas are ripe.
it means that if there are 100 apples, 20 are ripe.
Let the total number of cupcakes sold that day be X
20% of total number of cupcakes sold = 20% of X = (20/100) * X __1
It is given that 20% of total number of cupcakes sold is equal to 100
Thus the equation 1 should be equal to 100.
Writing it mathematically we have
(20/100) * X = 100
=> 0.2X = 100
=> X = 100/0.2 = 500
500 cupcakes did the bakery sell that day.
need math help please!!
Answer:
3
Step-by-step explanation:
That BD is a bisector means the angles on either side of it are congruent.
9x = 8x +3
x = 3 . . . . . . . subtract 8x
The value of x is 3.
The radius of the circle below intersects the unit circle at ( 3/5 • 4/5 What is the approximate value of e?
Answer:
12/25
Step-by-step explanation:
multiply the fractions.
multiply the numbers.
A jar is 25 filled with water. If 750 ml more water is poured into the jar, it becomes full. What is the capacity of the jar?
Answer:
775 ml
Step-by-step explanation:
Answer:
775
Step-by-step explanation:
25 plus 50 equals 75.700 plus 75= 775 ml.
Raj builds a side table in the shape of a cube. Each edge of the cube measures 30inches. Raj wants to cover the top and four sides of the table with ceramic tiles. Each tile has an edge length of 6inches. How many tiles will we need?
Answer:
deportation
Step-by-step explanation:
deport raj
Use the given values of n and p to find the minimum usual value μ - 2σ and the maximum usual value μ + 2σ.
n = 2136, p = 3/7
Answers:
1. Minimum: 843.1; maximum: 987.75
2. Minimum: 961.17; maximum: 869.69
3. Minimum: 892.56; maximum: 938.3
4. Minimum: 869.69; maximum: 961.17
Answer:
[tex] \mu -2\sigma = 915.428 - 2* 22.87=869.69[/tex]
[tex] \mu +2\sigma = 915.428 + 2* 22.87=961.17[/tex]
And the best option would be:
4. Minimum: 869.69; maximum: 961.17
Step-by-step explanation:
We can assume that the variable of interst X is distributed with a binomial distribution and we can use the normal approximation.
For this case the mean would be given by:
[tex] E(X) = np = 2136 *(\frac{3}{7})= 915.428[/tex]
And the standard deviation would be:
[tex] \sigma = \sqrt{2136*(\frac{3}{7}) (1-\frac{3}{7})} =22.87[/tex]
And if we find the limits we got:
[tex] \mu -2\sigma = 915.428 - 2* 22.87=869.69[/tex]
[tex] \mu +2\sigma = 915.428 + 2* 22.87=961.17[/tex]
And the best option would be:
4. Minimum: 869.69; maximum: 961.17
Including Jose, there are eight people in his family.
If order matters, how many ways can he arrange his family members into a row of five seats if Jose must sit in the first seat?
O 35
O 840
O 1,680
0 2,620
Answer:
840
Step-by-step explanation:
Since the order matters, we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
The first seat is Jose's.
The remaining four are organized among the other 7 members. So
[tex]P_{(7,4)} = \frac{7!}{(7-4)!} = 840[/tex]
So the correct answer is:
840
Answer:
The answer is B on Edge 2020
Step-by-step explanation:
I did the Exam
Question 15 (5 points)
Find the distance between the points (-1/2,-8) and (-1/2,-2).
Answer:
6
Step-by-step explanation:
Since the x coordinates are the same, you only need to find the difference between the y coordinates. -2-(-8)=-2+8=6. Hope this helps!
The class of 2004 holds a reunion each year. In 2005, 87.5% of the 120 graduates attended. In 2006, 90 students went, and in 2007, 75 students went. About how many students do you predict went to the reunion in 2010
Answer:
15 students
Step-by-step explanation:
% of students attended reunion in 2005 = 87.5% of 120
no of students attended reunion in 2005 = 87.5/100 * 120 = 105.
no of students attended reunion in 2006 = 90
no of students attended reunion in 2007 = 75
So , the series for the given year is
105, 90, 75
we can see that this arithmetical progression series
in arithmetical progression series
common difference is = nth term - (n-1)th term
lets takes 3rd and second term as nth term and (n-1)th term
common difference(d) is =75 - 90 = -15
n th term for any arithmetical progression series is given by
nth term = a + (n-1) d
where a is the first term
n is the nth term
d is the common difference
we have to calculate number of students in reunion of of 2010
as reunion began from 2005
2005,2006,2007,2008,2009,2010
so, 2010 is 6th term in series of 105, 90, 75....
6th term = a + (n-1) d
a is 90
6th term = 90+ (6-1)* -15
6th term = 90+ (5)* -15 = 90 - 75 = 15.
Thus, 15 students will attend reunion of 2010
5,-5/2,5/4,-5/8 what is the 5th term
Answer: your answer would be 5/16th :)
Answer:
5/16
Step-by-step explanation:
The common ratio is -5/2 / 5 = -1/2
Xn = 5 × (-1/2)^(n-1)
X5 = 5 × (-1/2)^(5-1)
X5 = 5 × (-1/2)^(4) = 5/16
Use the definition of continuity and the properties of limits to show that the function
f(x) = x2 + 5(x - 2)7 is continuous at x = 3.
Answer:
Applied the definition and the limit.
They had the same result, so the function is continuous.
Step-by-step explanation:
At function f(x) is continuous at x = a if:
[tex]\lim_{x \to a} f(x) = f(a)[/tex]
In this question:
[tex]f(x) = x^{2} + 5(x-2)^{7}[/tex]
At x = 3.
[tex]\lim_{x \to 3} x^{2} + 5(x-2)^{7} = 3^{2} + 5(3-2)^{7} = 14[/tex]
[tex]f(3) = 3^{2} + 5(3-2)^{7} = 14[/tex]
Since [tex]\lim_{x \to 3} f(x) = f(3)[/tex], f(x) is continuous at x = 3.
A total of 484 tickets we’re sold for the school play. They Either adult or student tickets. There were 66 Fewer student tickets sold than adult tickets . How many adult tickets were sold?
Answer:
x + 61 = 411
Step-by-step explanation:
Let x = the number of adult tickets sold
Let x + 61 = the number of student tickets sold
x + x + 61 = 761
2x = 700
x = 350
The length of a box is 18 cm. How long is the box
Answer: 18 cm
Step-by-step explanation:
Length means the same thing as “long” so whatever the length is, that’s how long it is. In this case, 18 cm is the length, so that’s how long it is.
PLZ HELP
Which system of inequalities is shown in the graph?
A) 2x + 3y ≤ 5 and -3x + 2y < 6
B) 2x + 3y < 5 and -3x + 2y ≤ 6
C) 2x + 3y ≥ 5 and -3x + 2y > 6
D) 2x + 3y > 5 and -3x + 2y ≥ 6