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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

The scores on a standardized mathematics test for 8th-grade children in New York State form a normal distribution with a mean of μ = 70 and a standard deviation of σ = 10.

  1. a. What proportion of the students in the state have scores less than X = 75?
  2. b. If samples of n = 4 are selected from the population, what proportion of the samples will have means less than M = 75?
  3. c. If samples of n = 25 are selected from the population, what proportion of the samples will have means less than M = 75?

(a)

To determine

To find: The proportion of the students in the state have scores less than X=75.

Explanation

Given info:

The random variable X denote the children in New York State follow normal distribution with a mean of μ=70 and standard deviation of σ=10.

Calculation:

Z score:

z=Xμσ

Substitute the values in the above formula is as follows:

z=757010=0

(b)

To determine

To find: The proportion of the samples will have means less than M=75.

(c)

To determine

To find:   The proportion of the samples will have means less than M=75.

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