Question

Suppose a batch of steel rods produced at a steel plant have a mean length of 151 millimeters, and a variance of 64. if 116 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would be less than 151.81 millimeters?

Answer 1

The probability that the mean length of the sample rods would be less than 151.81 millimeters is 86.21%

How to determine the probability that the mean length is less than 151.81

From the question, we have the following parameters that can be used in our computation:

Mean = 151 mm

Variance = 64

using the above as a guide, we have the following:

Standard deviation, SD = √64

SD = 8

The standard error of the meanis calculated as

E = σ/√n

E = 8/√116

E = 0.7428 millimeters.

So, we have the z-score to be

z = (151.81 - 151)/0.7428

z = 1.09

Using the z table, we have the probability to be

P = 0.8621

Hence, the probability is 0.8621, or 86.21%