Chapter 7, Problem 21P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

The average age for licensed drivers in the county is μ = 40.3 years with a standard deviation of σ = 13.2 years.

- a. A researcher obtained a random sample of
*n*= 16 parking tickets and computed an average age of*M*= 38.9 years for the drivers. Compute the z-score for the sample mean and find the probability of obtaining an average age this young or younger for a random sample of licensed drivers. Is it reasonable to conclude that this set of*n*= 16 people is a representative sample of licensed drivers? - b. The same researcher obtained a random sample of
*n*= 36 speeding tickets and computed an average age of*M*= 36.2 years for the drivers. Compute the*z*-score for the sample mean and find the probability of obtaining an average age this young or younger for a random sample of licensed drivers. Is it reasonable to conclude that this set of*n*= 36 people is a representative sample of licensed drivers?

**(a)**

To determine

**To find:** The z-score for the sample mean.

**To find:** The probability of obtaining an average age this young or younger for a random sample of licensed drivers

**To check:** Whether it is reasonable to conclude the set of

Explanation

**Given info:**

The average age for licensed drivers in the country is

The sample mean is and the random sample is,

**Calculation:**

The z-score is used to transform any distribution in to standardized distribution with a predetermined mean and a predetermined standard deviation.

The formula to find the z-Score is,

Where,

Substitute the value 40.3 for

**(b)**

To determine

**To find:** The z-score for the sample mean.

**To find:** The probability of obtaining an average age this young or younger for a random sample of licensed drivers.

**To check:** Whether it is reasonable to conclude the set of

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