The average speed of cars passing a checkpoint is 60 miles per hour with a standard deviation of 8 miles per hour.Fifty (50)passing cars are clocked at random from this checkpoint.The probability that the sample mean will be between 57 and 62 miles per hour is:
A) 0.9576.
B) 0.9960.
C) 0.2467.
D) 0.3520.
E) 0.4659

Question

Quizplus · Accepted Answer

This problem can be solved using the Central Limit Theorem (CLT), which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough (n > 30 is a common rule of thumb), regardless of the shape of the population distribution. Given the population mean (μ) is 60 mph, the standard deviation (σ) is 8 mph, and the sample size (n) is 50, we can calculate the standard error of the mean (σ_x̄) as σ/√n = 8/√50. To find the probability that the sample mean is between 57 and 62 mph, we convert these values to Z-scores and use the standard normal distribution. The calculations show that the probability falls within this range, closely matching the value given in choice A, 0.9576, using standard normal distribution tables or a calculator.

The Average Speed of Cars Passing a Checkpoint Is 60