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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

The SAT scores for the entering freshman class at a local college form a normal distribution with a mean of μ = 530 and a standard deviation of σ = 80.

  1. a. For a random sample of n = 16 students, what range of values for the sample mean would be expected 95% of the time?
  2. b. What range of values would be expected 95% of the time if the sample size were n = 100?

(a)

To determine

To Find: The range of values for the sample mean would be expected 95% of the time.

Explanation

Given info:

The sample of n=25 students is selected from a population with a mean of μ=530 and standard deviation of σ=80.

Calculation:

The formula for calculating the z-score is,

z=MμσM

Where, σM=σn.

The standard error is,

σM=8016=20

The range of values for the sample mean would be expected 95% of the time is,

For z=+1

(b)

To determine

To find: The range of values for the sample mean would be expected 95% of the time.

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