Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 125 millimeters, and a standard deviation of 7
millimeters.
If a random sample of 44 steel bolts is selected, what is the probability that the sample mean would be greater than 127.1 millimeters? Round your
answer to four
decimal places

Answer 1

Answer:

P(X > 127.1) = 0.0233

Step-by-step explanation:

We are given;

Population mean; μ = 125 mm

Sample mean; x¯ = 127.1 mm

Sample size; n = 44

Standard deviation; σ = 7 mm

Formula for test statistic is;

z = (x¯ - μ)/(σ/√n)

z = (127.1 - 125)/(7/√44)

z = 2.1/1.0553

z = 1.99

From z-table attached;

P(X > 127.1) = P(z > 1.99) = 1 - 0.97670 = 0.0233