The lifetime of battery of a device (in one charge) is normally distributed with mean µ = 18 hours and standard deviation σ = 2 hours. (a) What is the probability that a battery will last more than 20 hours? (b) Find the 10th percentile of the lifetimes. (c) A particular battery lasts 16 hours. What percentile is its lifetime on? (d) What is the 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?

Answers

Answer 1

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


Related Questions

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Step-by-step explanation:

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Step-by-step explanation:

This is a very simple explanation.

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Step-by-step explanation:

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Step-by-step explanation:

Here

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Five houses in the neighborhood sold this month for the following prices:
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Answers

Answer:

70,000

Step-by-step explanation:

Median= 345,000

Higest selling house= 415,000

415,000-345,000= 70,000

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Answers

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$20.00

Answers

Answer:

$ 14.00

Step-by-step explanation:

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17.50 · .20 = 3.5

17.50 - 3.50 = 14.00

good luck, i hope this helps :)

Use the number line to complete the statements.
The opposite of 4 is ____.
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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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

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Answers

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.

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Answers

Answer:

118

Step-by-step explanation:

118.385

  |

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118

Step-by-step explanation:

118.385

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Answer:

Percent, Part, whole, I am not sure the rest hope this helped though

Step-by-step explanation:

Answer:

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Answer:

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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.

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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.

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Answers

Answer:

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Use the drop-down menus to show your answer.

WILL GIVE BRANLIEST IF ANSWERED

Answers

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

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Function B: y = 3x - 1

Function C: y = 1/3x + 2

Then graph of the functions is given below.

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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

What is the solution to the system of equations graphed below?

y = 4x + 11

y = -2x - 1

Answers

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).

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

Answers

*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.

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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

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Answers

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

Can someone help me I don’t know how to do this it’s hard and confusing me

Answers

9514 1404 393

Answer:

increasing on 0 < x < 2f(2) = 4decreasing on 2 < x < 5

Step-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.

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?

Answers

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.

I don't know what to do ​

Answers

120°, thinking logically it’s bigger than 90° but not big enough to be over 150°, so your last answer is 120°
That’s a 120 degree
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