High School

According to the National Highway Traffic Safety Administration, the average age of drivers who were involved in a fatal crash is 39.4 years, with a standard deviation of 17.4 years. Suppose a random sample of 50 drivers involved in a fatal crash is selected.

1. What is the probability that the average age of drivers involved in a fatal crash in the sample exceeds 41?
A. 0.4641
B. 0.6504
C. 0.2578
D. 0.7422
E. 0.5359

2. We expect the average age from the sample to be around --- give or take.
A. EV = 1970; SE = 123.0479
B. EV = 39.4; SE = 17.4154
C. EV = 278.60; SE = 123.0411
D. EV = 2.46; SE = 39.4054
E. EV = 39.4; SE = 2.4607

[Source: https://crashstats.nhtsa.dot.gov/Api/Public/ViewPublication/810853]

Answer :

The probability that the average age of drivers involved in a fatal crash in the sample exceeds 41 is 0.2578.

To find the probability that the average age of drivers involved in a fatal crash in the sample exceeds 41, we can use the concept of the sampling distribution of the sample mean. Since the sample size is large (n > 30) and the population standard deviation is known, we can use the z-distribution.

First, we calculate the standard error (SE) of the sample mean using the formula:

SE = population standard deviation / sqrt(sample size)

SE = 17.4 / sqrt(50) ≈ 2.4607

Next, we calculate the z-score using the formula:

z = (sample mean - population mean) / SE

z = (41 - 39.4) / 2.4607 ≈ 0.651

Finally, we find the probability that the z-score is greater than 0.651 in the standard normal distribution table. The probability is approximately 0.2578.

Therefore, the correct answer is 0.2578.

Learn more about Probability here:

https://brainly.com/question/22962752

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