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A large car insurance company is conducting a study on behavior behind the wheel to explain the fact that male drivers (who tend to be thought of as more aggressive drivers) have more accidents, on average, per year, than female drivers. The average number of accidents per year for male drivers is 2.3 with a standard deviation of 0.8 and for female drivers the mean is 1.7 with a standard deviation of 0.6. Independent random samples of 25 male and 20 female drivers are to be selected to take part in the behavior study.
-Suppose we can assume that the number of accidents per year is normally distributed, both for males and for females. What is the probability that the average number of accidents in the sample of 25 male drivers is less than the average number of accidents in the sample of 20 female drivers?
A)

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Use the following information for questions:
 A large car insurance company is conducting a study on behavior behind the wheel to explain the fact that male drivers (who tend to be thought of as more aggressive drivers) have more accidents, on average, per year, than female drivers. The average number of accidents per year for male drivers is 2.3 with a standard deviation of 0.8 and for female drivers the mean is 1.7 with a standard deviation of 0.6. Independent random samples of 25 male and 20 female drivers are to be selected to take part in the behavior study.
-Suppose we can assume that the number of accidents per year is normally distributed, both for males and for females. What is the probability that the average number of accidents in the sample of 25 male drivers is less than the average number of accidents in the sample of 20 female drivers?
A) < 0.0001
B) 0.0020
C) 0.0207
D) 0.2266

Quizplus · Accepted Answer

The probability is calculated using the difference in sample means, which follows a normal distribution. The mean difference is 0.6, and the standard deviation of the difference is approximately 0.213. Using the standard normal distribution, the probability that the male sample mean is less than the female sample mean is approximately 0.0020.

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