Answer:
a) 0.1587 = 15.87% probability that a battery will last more than 20 hours.
b) 15.44 hours.
c) Approximately the 16th percentile.
d) 0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.
e) 0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question, we have that:
[tex]\mu = 18, \sigma = 2[/tex]
(a) What is the probability that a battery will last more than 20 hours?
This is 1 subtracted by the pvalue of Z when X = 20. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 18}{2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that a battery will last more than 20 hours.
(b) Find the 10th percentile of the lifetimes.
This is X when Z has a pvalue of 0.1. So X when Z = -1.28
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 18}{2}[/tex]
[tex]X - 18 = -1.28*2[/tex]
[tex]X = 15.44[/tex]
So 15.44 hours.
(c) A particular battery lasts 16 hours. What percentile is its lifetime on?
We have to find the pvalue of Z when X = 16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 18}{2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
Approximately the 16th percentile.
(d) What is the probability that the lifetime of a battery is between 17.5 and 18.5?
This is the pvalue of Z when X = 18.5 subtracted by the pvalue of Z when X = 17.5. So
X = 18.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18.5 - 18}{2}[/tex]
[tex]Z = 0.25[/tex]
[tex]Z = 0.25[/tex] has a pvalue of 0.5987
X = 17.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{2}[/tex]
[tex]Z = -0.25[/tex]
[tex]Z = -0.25[/tex] has a pvalue of 0.4013
0.5987 - 0.4013 = 0.1974
0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.
(e) Ten batteries are chosen at random, what is the probability that the mean lifetime is between 17.5 and 18.5?
Sample of 10 means that, by the Central Limit Theorem, [tex]n = 10, s = \frac{2}{\sqrt{10}} = 0.6325[/tex]
X = 18.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18.5 - 18}{0.6325}[/tex]
[tex]Z = 0.79[/tex]
[tex]Z = 0.79[/tex] has a pvalue of 0.7852
X = 17.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.5 - 18}{0.6325}[/tex]
[tex]Z = -0.79[/tex]
[tex]Z = -0.79[/tex] has a pvalue of 0.2148
0.7852 - 0.2148 = 0.5704
0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5
The zoo has 4 tigers and plans to adopt more tigers soon. Gabby meets with Chloe, the manager of the tiger exhibit, to discuss the tigers’ habitat. They want to make sure there is enough space for the new tigers.
The Natureland Zoo has these requirements for a tiger habitat:
The trees, feeding station, and drinking station need at least 300 square feet all together.
Each tiger needs at least 225 square feet of space.
How many square feet of space is the zoo required to have for 4 tigers? Show your work.
Answer:
multiple 4×225 because there are 4 tigers and one Tiger needs 225 square feet so mutiple 4×225 and you got 900 so the answer will be 900 square feet
Which linear function has the greatest initial value? Which has the greatest rate of change?
Use the drop-down menus to show your answer.
WILL GIVE BRANLIEST IF ANSWERED
The linear function C has the greatest initial value is 2. And the linear function B that has the greatest rate of change is 3.
The complete question is attached below.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
Then the equations of the functions A, B, and C is given as
Function A: y = 5/2 x
Function B: y = 3x - 1
Function C: y = 1/3x + 2
Then graph of the functions is given below.
The linear function C has the greatest initial value is 2.
The linear function B that has the greatest rate of change is 3.
More about the equation of line link is given below.
https://brainly.com/question/21511618
#SPJ1
How much will the class members earn if they spend six weeks doing yard work? How much will they earn if they spend six weeks having a car wash
How many miles will Mrs. Garcia drive in eight hours if she is traveling 65 mph? _ miles
Answer:
she would probably drive 520 miles in she is driving 65 mph for a whole 8 hours
Step-by-step explanation:
Answer:
520
Step-by-step explanation:
This is a very simple explanation.
Mrs. Garcia drives eight hours...at 65mphs throughout the trip.
How many miles has she drove?
All you need to do is multiply 8x65 and you will get 520.
Mrs. Garcia drove a total of 520 miles.
Hank’s Fried Chicken has $1,692 extra this month to give its employees as a bonus. Each employee received $53 as their bonus. How many people work for Hank’s Fried Chicken?
Given:
Total amount of bonus = $1,692
Bonus received by each employee = $53
To find:
The Number of people work for Hank’s Fried Chicken.
Solution:
We need to divide the total bonus by the bonus of each employee to get the number of people work for Hank’s Fried Chicken.
[tex]\text{Number of people}=\dfrac{\text{Total amount of bonus}}{\text{Bonus received by each employee}}[/tex]
[tex]\text{Number of people}=\dfrac{1692}{53}[/tex]
[tex]\text{Number of people}=31.92453[/tex]
Number of people must be whole number. So, approx the value to the preceding whole number.
[tex]\text{Number of people}\approx 31[/tex]
Therefore, 31 people work for Hank’s Fried Chicken.
change the following improper to mixed plz help quick!
1. 8/3
2. 9/4
3. 12/5
Answer:
Improper Fractions:
Step-by-step explanation:
1. 2 and 2/3
2. 2 and 1/4
3. 2 and 2/5
I don't know what to do
f(x)= 3x+10 and g(x)= 3x-7
Answer:
1. x=-10/3
2. x=7/3
Step-by-step explanation:
plsssssssss mark me brainliest I need one more
A report describes the results of a large survey that was conducted for the Center for Disease Control (CDC). The sample was selected in a way that the CDC believed would result in a sample that was representative of adult Americans. One question on the survey asked respondents if they had learned something new about a health issue or disease from a TV show in the previous 6 months. Data from the survey was used to estimate the following probabilities, where
L = outcome that a randomly selected adult American reports learning something new about a health issue or disease from a TV show in the previous 6 months
and
F = outcome that a randomly selected adult American is female
Data from the survey were used to estimate the following probabilities:
P(L)= 0.58 P(F)= 0.50 P(L and F)= 0.31
Are the outcomes L and F independent? Use probabilities to justify your answer.
Answer:
Since [tex]P(L \cap F) \neq P(L)P(F)[/tex], the outcomes L and F are not independent.
Step-by-step explanation:
Independent events:
Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Are the outcomes L and F independent?
We are given that:
[tex]P(L \cap F) = 0.31[/tex]
Multiplication of the probabilities:
[tex]P(L)P(F) = 0.58*0.5 = 0.29[/tex]
Since [tex]P(L \cap F) \neq P(L)P(F)[/tex], the outcomes L and F are not independent.
Five houses in the neighborhood sold this month for the following prices:
$328,000, $297,500, $415,000, $389,000, $345,000.
The house with the highest selling price sold for how much more than the median selling price?
Answer:
70,000
Step-by-step explanation:
Median= 345,000
Higest selling house= 415,000
415,000-345,000= 70,000
The temperature at 7 a.m. was -11°C. The temperature increased by 9°C during the
day arid then decreased by 4°C at 8 p.m. Which was the temperature at 8 p.m.?
Help!! Pythagorean theorem
Answer:
The Pythagorean theorem only works for right triangles. This is not a right triangle.
x = 23
All interior angles of a triangle = 180 degrees.
A + B + C + 180
(3x) + (2x+12) + (2x+7) = 180
7x + 19 = 180
7x = 161
x = 23
A = 3(23) = 69 degrees
B = 2(23) + 12 =58 degrees
C = 2(23) + 7 = 53 degrees
Answer:
x=23
Step-by-step explanation:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Help
a.66 b.124 c.114 d.132
Answer:
probably 66, because if m<CDA = 66 then so does m<BCD because they're both the same lengths
Can someone help me I don’t know how to do this it’s hard and confusing me
9514 1404 393
Answer:
increasing on 0 < x < 2f(2) = 4decreasing on 2 < x < 5Step-by-step explanation:
You need to know that an even function is symmetrical about the y-axis. The graph to the right of the y-axis is the mirror image of the graph to the left. With that in mind, the questions are easily answered.
It might help to draw the function graph, as we did in the attached. Then it is more straightforward to see what is happening in each of the intervals.
The function is increasing in the interval 0 < x < 2.
The function value at x=2 is 4: f(2) = 4.
The function is decreasing in the interval 2 < x < 5.
Write the expression 12 x 4^2 in words
Answer and Step-by-step explanation:
Twelve times four squared.
This is how you would write the expression in word format.
#teamtrees #PAW (Plant And Water)
Answer:
Twelve times four squared.
Step-by-step explanation:
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answer:
Yes
Step-by-step explanation:
So we substitute the point given x=-5 and y = -3 to see if this solves both equations at the same time so
3(-5) - 9(-3) = 12 -> -15+27 = 12 -> 12 = 12 [this one works]
8(-5) - 14 (-3) = 2 -> -40 + 42 = 2 -> 2=2 [this one works also]
Since (-5,-3) is a solution to both equations, then this is a solution to this system
Answer: Yes
Step-by-step explanation:
Here
x = -5
y = -3
3x - 9y = 12
Here if you substitute x and y,
3 * (-5) - 9 * (-3)
(-15) - (-27)
=12
8x - 14y = 2
8 * (-5) - 14 * (-3)
(-40) - (-42)
= 2
118.385 to the nearest ones
Answer:
118
Step-by-step explanation:
118.385
|
ones place
Answer:
118
Step-by-step explanation:
118.385
5 rounds 8 to 9
9 rounds 3 to 4
4 isnt 5 or above so 4 makes 8 stay the same
Can someone plz help me with my whole homework?
1.The original price is $20. The Percent of Discount is 20%. What is the sale price?
2.The original price is $95. The Percent of Discount is 35%. What is the sale price?
3.The Percent of Discount is 75%. The sale price is $55.50. What is the original price?
4.The Percent of Discount is 40%. The sale price is $78. What is the original price?
5.Find the selling price. The cost to store: $20. The markup: 15%.
6.Find the selling price. The cost to store: $56. The markup: 80%.
7.Find the selling price. The cost to store: $110. The markup: 140%.
8.A store buys an item for $10. To earn a profit of $25, what percent does the store need to markup the item?
9.An account earns simple interest. Find the interest earned.
$400 at 7% for 3 years
10.An account earns simple interest. Find the balance of the account.
$400 at 7% for 3 years
11.An account earns simple interest. Find the interest earned.
$1200 at 5.6% for 4 years
12.An account earns simple interest. Find the balance of the account.
$1200 at 5.6% for 4 years
13.Find the annual interest rate.
I = $18, P = $200, t = 18 months
14.Find the annual interest rate.
I = $310, P = $1000, t = 5 years
15.Find the amount of time.
I = $60, P = $750, r = 4%
16.Find the amount of time.
I = $825, P = $72500, r = 5.5%
17.You put $500 in a savings account. The account earns $15.75 simple interest in 6 months. What is the annual interest rate?
Answer:
Step-by-step explanation:
Answer:
people may not be doing it because u have it up for 5 points and it is alot of work.
Step-by-step explanation:
the difference of 17 and 5 times a number
Answer:
I need more context
Step-by-step explanation:
I need help doing this please
Step-by-step explanation:
what is the question asking
Brenda sells necklaces at the 23rd Street Flea market. It costs her $10.00 in materials to make the necklaces. She decides to mark-up the price of her ned
by 75% to make a profit. An hour before the flea market closes she decided to reduce the leftover necklaces by 20% from the morning's price. How much
she selling her necklaces at the end of the day?
$20.00
Answer:
$ 14.00
Step-by-step explanation:
10 · 1.75 = 17.50
17.50 · .20 = 3.5
17.50 - 3.50 = 14.00
good luck, i hope this helps :)
Which number line shows the solution to the inequality 9x-4<5? I NEED IT ASAP PLSS free 15 points
Answer:
B would be your answer I think Don't hold me to it!
Step-by-step explanation:
Answer:B -4-2 0 2 4
Step-by-step explanation:
The figure shown has two parallel lines cut by a transversal: A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left. Use the figure to complete the sentence. ∠7 and ____ are alternate exterior angles. ∠2 ∠1 ∠5 ∠8
*see attachement for the diagram of the figure being referred to
Answer:
<1
Step-by-step explanation:
Alternate exterior angles are a pair of angles which are located on the opposite side of the transversal, outside the two parallel lines.
From the figure given, you would see that <7 and <1 lie on opposite side of the transversal and they lie on the outside of the two parallel lines that are cut across by the transversal.
Therefore:
<7 and <1 are alternate exterior angles.
Use the number line to complete the statements.
The opposite of 4 is ____.
(1). -8
(2). -4
(3). 0
(4). 4
The opposite of –8 is _____.
(1). -8
(2). 0
(3). 4
(4). 8
Answer:
(2). -4
(4). 8
Step-by-step explanation:
The opposite of a negative or positive number will always be it's absolute value.
CAN SOMEONE HELP PLEASE ASAP!!! ILL MAKE YOU BRAINLIEST
Answer:
I think the answer is D but I'm not 100 percent sure. I hope this helps
Step-by-step explanation:
I think I took this test before
Write the fraction 1/5 as a percent.
Answer:
20%
Step-by-step explanation:
help me please asap!!!
Answer:
122°
Step-by-step explanation:
<ADC is an inscribed angle and its measure is equal to half of the arc it sees (minor arc AC)
if ADC is 61° then minor arc AC is 2 × 61 = 122
ABC is the center angle and so its measure is equal to the arc it sees which is 122°
I need the answer please help
Answer:
Check pdf
Step-by-step explanation:
Help plsssss!!!!!!!!!!!!!
Answer:
Percent, Part, whole, I am not sure the rest hope this helped though
Step-by-step explanation:
Answer:
15% is the percent, 9$ is the part and the original price is the whole
the original price is 60$ and the coustomer buys it for 51$
What is the solution to the system of equations graphed below?
y = 4x + 11
y = -2x - 1
Answer:
Step-by-step explanation:
y = 4x + 11, and y = -2x - 1, so
4x + 11 = -2x - 1
6x + 11 = -1
6x = -12
x = -2
y = 4x+11 = 3
y = 4x + 11
y = -2x - 1
4x + 11 = -2x - 1
4x + 2x = -1 - 11
6x = -12
x = -12/6
x = -2
y = 4x + 11
y = 4(-2) + 11
y = -8 + 11
y=3
Answer is (-2,3).