Answer:
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,
