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Chapter 7: Q.21 (page 428)

Find the probability that the sums will fall between the z-scores –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:

∑X=(n)μX+(z)(n)σX

=100×39.01−2×100×0.5

=3891

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

ΣX=(n)μX+(z)(n)σx

=100×39.01+1×100×0.5

=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

An unknown distribution has a mean of 80and a standard deviation of 12. A sample size of 95is drawn randomly from the population.

Find the probability that the sum of the 95values is greater than 7650.

According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040is 10.53hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36taxpayers.

a. In words, Χ=_____________

b. In words,X=_____________

c. X¯~_____(_____,_____)

d. Would you be surprised if the 36taxpayers finished their Form 1040s in an average of more than 12hours? Explain why or why not in complete sentences.

e. Would you be surprised if one taxpayer finished his or her Form 1040in more than 12hours? In a complete sentence, explain why.

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¯~

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¯. Shade the region corresponding to the probability. Find the probability.

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

What is the z-score for Σx = 1,186?

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c.0.0943

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