The inside diameter of a randomly selected piston ring is a random variable with mean value 14 cm and standard deviation 0.05 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.) (a) Calculate P(13.99 ≤ X ≤ 14.01) when n = 16. P(13.99 ≤ X ≤ 14.01) = 0.4207 Incorrect: Your answer is incorrect. (b) How likely is it that the sample mean diameter exceeds 14.01 when n = 25? P(X ≥ 14.01) = 0.4207 Incorrect: Your answer is incorrect. Y

a) 0.5762

b) 0.1587

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 14 cm

Standard Deviation, σ = 0.05 cm

We are given that the distribution of diameter is a bell shaped distribution that is a normal distribution.

Formula:

a) P(13.99 ≤ X ≤ 14.01 when n = 16)

Standard error due to sampling =

b) P(sample mean diameter exceeds 14.01 when n = 25)

Standard error due to sampling =

Calculation the value from standard normal z table, we have,  

p = 6s

step-by-step explanation: