(a) Calculate the z-score for a man's hip breadth of 14.4 inches using the formula:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
where x is the value (14.4 inches in this case), mu is the mean (14.4 inches), and sigma is the standard deviation (1 inch).
Substituting the values:
[tex]z = \frac{14.4 - 14.4}{1} = 0[/tex]
So, the z-score for a man's hip breadth of 14.4 inches is 0.
(b) To find the proportion of men with hip breadths less than 16.2 inches, we need to find the z-score corresponding to 16.2 inches and then find the area under the normal curve to the left of that z-score.
Using the same formula:
[tex]z = \frac{16.2 - 14.4}{1} = 1.8[/tex]
Now, we need to find the proportion of values less than z = 1.8 using a standard normal distribution table or a calculator.
(c) Interpret the result from part (b) in the context of the problem.
This proportion tells us the percentage of men whose hip breadths are smaller than the seat width of 16.2 inches. It gives us an idea of how many men might find the seats comfortable due to their hip breadth being less than the seat width.