Chapter 7, Problem 14P

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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.

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

Explanation

**Given info:**

The random variable X denote the children in New York State follow normal distribution with a mean of

**Calculation:**

*Z score:*

Substitute the values in the above formula is as follows:

**(b)**

To determine

**To find:** The proportion of the samples will have means less than

**(c)**

To determine

**To find: ** The proportion of the samples will have means less than

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