probability statistics

Question

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.2-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.2% or largest 1.2%.

What is the minimum head breadth that will fit the clientele? 

min = Incorrect

What is the maximum head breadth that will fit the clientele? 

max = Incorrect

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Consider the z-table. Find the z-score associated with an area of 0.012 in the left tail, and then the z-score associated with 0.012 in the right tail. In your case, use the formula (equation)

z-score = (x - 6.2)/1; that is, x = z + 6.2, in both instances. That should produce your solution.