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Chapter 6: Q.6.59 (page 388)

The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years

Find the 70thpercentile of the distribution for the time a CD player lasts

a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the lower 70%.

b. P(x<k)=__________Therefore,k=_________

Short Answer

Expert verified
  1. The graph for the 70thpercentile is shown below

b. The value of 70thpercentile isP(x<k)=0.70andk=4.78172.

Step by step solution

01

Step: Given information (Part a)

Given in the question that

Mean=4.1

Standard deviation=1.3

02

solution (Part b)

The graph for the 70thpercentile

That is P(x<k)=0.70and it has been shown as a shaded region in the below graph

03

Given information (Part b)

Given in the question that

Mean=4.1

Standard deviation=1.3

04

Solution (part b)

The probability can be calculated as

P(x<k)=0.70

It can be calculated below

P(x<k)=Px鈭�渭蟽<k鈭�渭蟽

0.70=PZ<k鈭�4.11.3

k鈭�4.11.3=0.5244From standardnormal table

k鈭�4.1=0.5244脳1.3

k=0.6817+4.1

k=4.78172

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Most popular questions from this chapter

We flip a coin \(100\) times \((n = 100)\) and note that it only comes up heads \(20% (p = 0.20)\) of the time. The mean and standard deviation for the number of times the coin lands on heads is \(\mu=20\) and \(\sigma=4\) (verify the mean and standard deviation). Solve the following:

a. There is about a \(68%\) chance that the number of heads will be somewhere between ___ and ___.

b. There is about a ____chance that the number of heads will be somewhere between \(12\) and \(28\).

c. There is about a ____ chance that the number of heads will be somewhere between eight and \(32\).

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

a. If X=distance in feet is for a fly ball, then X~

b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball will travel fewer than 220 feet? Sketch the graph. Scale the horizontal axis XShade the region corresponding to the probability. Find the probability.

c. Find the 80ithpercentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

A The distance of fly balls hit to the outfield in baseball is denoted as: N~N(250,50)

B: The probability that a randomly selected fly ball traveled fewer than 220 feet is given by P(x<220)=0.2743

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.

What is the z-score for a patient who takes ten days to recover?

a. 1.5

b. 0.2

c. 2.2

d. 7.3

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.

Find the probability that it takes at least eight minutes to find a parking space.

a. 0.0001

b. 0.9270

c. 0.1862

d. 0.0668

Use the following information to answer the next two exercises: The life of Sunshine CD players is normally distributed with mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts.

X~_____(_____,_____)
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