Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 136 millimeters, and a standard deviation of 7 millimeters. If a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 2.1 millimeters?

Answer 1

The mean diameter and standard deviation for the sample can be calculated using the given formulas. The probability of the sample mean differing from the population mean within the stated tolerance levels can be calculated using the z-score and the standard normal distribution table. The company's diameter claim is plausible because the probability is 50%.

Step-by-step explanation:

To find the mean diameter and standard deviation for the sample, we use the formulas:

Sample Mean = Population Mean = 136 millimeters

Sample Standard Deviation = Population Standard Deviation / sqrt(n) = 7 millimeters / sqrt(35) = 1.18 millimeters

To find the probability that 50 randomly selected screws will be within the stated tolerance levels, we need to calculate the z-score and find the corresponding probability using the standard normal distribution table. The z-score is calculated as:

Z = (Sample Mean - Population Mean) / (Population Standard Deviation / sqrt(n)) = (136 - 136) / (7 / sqrt(35)) = 0

Since the z-score is 0, the probability is 0.5 or 50%. Therefore, the company's diameter claim is plausible.