Help with statistics, please!

Question

Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6-in and a standard deviation of 1.1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 1.3% or largest 1.3%.

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

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

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

If you have a TI-84, use the 'distr" key (blue 2nd button / "vars") then "3:invNorm". For the area, enter 0.974 (which is 1 - 0.013•2). For μ, enter "6" (the mean). For σ, enter 1.1 (the standard deviation), For the "tail" enter "CENTER" (since the area in question is centered around the mean. Then select "paste" and "enter" and you will get the answer (3.551167056, 8,448832944) which, interpreted, is that the smallest size is 3.6" and the largest size is 8.4".