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Chapter 7: Q.23 (page 428)

What is the standard deviation of ΣX?

Short Answer

Expert verified

The standard deviation ofΣX=5.

Step by step solution

01

Given Information

An unknown distribution has a mean 12and a standard deviation of one. A sample size of 25 is taken. Let X = the object of interest.

02

Explanation

The standard deviation is the dimensions of the portion of interpretation or disbandment of a cluster of matters.

The standard deviation of ΣXis :

=n(σx)

25×1

=5

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Most popular questions from this chapter

Find the probability that the sum of the 40 values is less than 7,000.

Salaries for teachers in a particular elementary school district are normally distributed with a mean of\(44,000and a standard deviation of \)6,500. We randomly survey ten teachers from that district.

a. Find the90thpercentile for an individual teacher’s salary.

b. Find the 90thpercentile for the average teacher’s salary.

Find the percentage of sums between1.5standard deviations below the mean of the sums and one standard deviation above the mean of the sums.

Yoonie is a personnel manager in a large corporation. Each month she must review 16of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2hours. Let Χ be the random variable representing the time it takes her to complete one review. Assume Χ is normally distributed. Let x-be the random variable representing the meantime to complete the 16reviews. Assume that the 16reviews represent a random set of reviews.

Find the probability that one review will take Yoonie from 3.5to 4.25hours. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability

b. P(________ <x< ________) = _______

What three things must you know about distribution to find the probability of sums?
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