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Chapter 7: Q.21 (page 428)

Find the probability that the sums will fall between the z-scores 鈥�2 and 1.

Short Answer

Expert verified

The required probability is0.8186.

Step by step solution

01

Given Information

Given in the question that, the sample size of 100is randomly drowned from cans of the same soda with mean39.01and the standard deviation is0.5

02

Explanation

The sum that is z-score-2standard deviation is:

鈭�X=(n)渭X+(z)(n)蟽X

=100脳39.01鈭�2脳100脳0.5

=3891

Let's compute the sum that is z-score-1standard deviation is:

危X=(n)渭X+(z)(n)蟽x

=100脳39.01+1脳100脳0.5

=3906

03

Using Ti-83 calculator

To find the proportion of sums, we'll use the Ti-83 calculator:

To do so, go to 2nd, then DISTR.

Then, scroll down to the normalcdf option and fill in the required information.

After that, press the calculator's enter button to get the result.

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Most popular questions from this chapter

A typical adult has an average IQ score of 105with a standard deviation of 20. If 20randomly selected adults are given an IQ test, what are the probability that the sample mean scores will be between 85 and 125 points?

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. We randomly sample 49 fly balls.

a. If Xthe average distance in feet for 49 fly balls, then X炉~

b. What is the probability that the 49 balls traveled an average of fewer than 240 feet? Sketch the graph. Scale the horizontal axis forX炉. Shade the region corresponding to the probability. Find the probability.

c. Find the 80thpercentile of the distribution of the average of 49 fly balls.

For the sums of distribution to approach a normal distribution, what must be true?

Find the sum that is 1.5 standard deviations below the mean of the sums.

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

What is the distribution for the mean length of time 64 batteries last?
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