Question

Question 2: [15 marks, 5 each] Manufacturing and Product Development:
The actual width of a 2×4 piece of lumber is approximately 1 3/4 in (1.75 in). but can vary considerably. Larry’s Lumber advertises consistent dimensions for better building, and claims all 2×4 sold have a mean width of 1 3/4 in. with a standard deviation of 0.02 in.
a. [5 marks] Assume the distribution of widths is approximately normal. Find a symmetric interval about the mean that contains almost all of the 2×4 widths. Show your work. (1.75
b. [5 marks] Suppose a random 2×4 has width 1.78 in. Is there any evidence to suggest the Larry’s Lumber claim is wrong? Justify your answer.
c. [5 marks] Suppose a random 2×4 has width 1.68 in. Is there any evidence to suggest the Larry’s Lumber claim is wrong? Justify your answer.

Answer 1

Thre symmetric data is shown on normal distribution graph below

There is no enough evidence to prove that the Lary's Lumber claim is  wrong.

Thus we accept the null hypothesis and reject the alternate hypothesis.

And the clain that mean is 1.75 inches is correct

Here we have enough evidence to reject the null hypothesis and accept the alternate hypothesis that the mean of lumber width is different from 1.75inches.