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Chapter 7: Q. 29 (page 429)

An unknown distribution has a mean of 25 and a standard deviation of six. Let X = one object from this distribution. What is the sample size if the standard deviation of 危X is 42?

Short Answer

Expert verified

The sample size is used to calculate the number of individuals in a particular area in statistical terms.

Step by step solution

01

Given information

The mean of the unknown distribution is25and the standard deviation is six and the standard deviation of鈭�Xis42. The formula for the standard deviation is;

鈭�X=(n)(蟽X)

The sample size is;

42=n脳6

n=426

n=7

n=49

02

Final answer

The sample size for the given distribution is49.

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Most popular questions from this chapter

Use the information in Example \(7.9\), but change the sample size to \(144\).

a. Find \(P(20<\bar{x}<30)\).

b. Find \(P(\sum x\) is at least \(3,000)\).

c. Find the \(75th\) percentile for the sample mean excess time of \(144\) customers.

Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of \(0.88. Suppose that we randomly pick 25daytime statistics students.

a. In words,围=____________

b.围~_____(_____,_____)

c.role="math" localid="1651578876947" Inwords,X=____________

d. X~______(______,______)

e. Find the probability that an individual had between \)0.80and\(1.00. Graph the situation, and shade in the area to be determined.

f. Find the probability that the average of the 25 students was between \)0.80and$1.00. Graph the situation, and shade in the area to be determined.

g. Explain why there is a difference in part e and part f.

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 less than 7400.

An unknown distribution has a mean of 25 and a standard deviation of six. Let X = one object from this distribution. What is the sample size if the standard deviation of 危X is 42?

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.
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