The lengths of lumber a machine cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.5 inch. (a) what is the probability that a randomly selected board cut by the machine has a length greater than 95.15 inches? (b) a sample of 45 boards is randomly selected. what is the probability that their mean length is greater than 95.15 inches?

a) 0.382

b) 0.021

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 95 inches

Standard Deviation, σ = 0.5 inch

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 95.15 inches)

P(x > 95.15)

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

0.382  is the probability that a randomly selected board cut by the machine has a length greater than 95.15 inches.

b) Standard error due to sampling

P( length greater than 95.15 inches in sample)

P(x > 95.15)

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

0.021  is the probability that their mean length of the sample is greater than 95.15 inches.

(x+3)(x+7)

step-by-step explanation: