The lengths of lumber a machine cuts are normally distributed with a mean of 100 inches and a standard deviation of 0.3 inch. (a) what is the probability that a randomly selected board cut by the machine has a length greater than 100.12 inches? (b) a sample of 41 boards is randomly selected. what is the probability that their mean length is greater than 100.12 inches?

a) 0.345

b) 0.005

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 0.3

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

Formula:

a) P(length greater than 100.12 inches)

P(x > 100.12)

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

b) Standard error due to sampling:

P(length greater than 100.12 inches for the sample)

P(x > 100.12)

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

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step-by-step explanation: