Question

The lengths of screws produced by a machine are normally distributed with a mean of 75 mm and a standard deviation of 0.1 mm. What is the probability that a randomly selected screw is longer than 75.2 mm?

A. 0.16

B. 0.34

C. 0.84

D. 0.50

Answer 1

To find the probability that a randomly selected screw is longer than 75.2 mm, we need to calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that a randomly selected screw is longer than 75.2 mm, we need to calculate the z-score and then use the standard normal distribution table.

The z-score formula is: z = (x - mean) / standard deviation

Substituting the given values, we get: z = (75.2 - 75) / 0.1 = 2

Looking up the z-score value of 2 in the standard normal distribution table, we find that the area to the right of 2 is approximately 0.0228. Therefore, the probability that a randomly selected screw is longer than 75.2 mm is approximately 0.0228.