SOLUTION: 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 a

Question 1167695: 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 5.9-in and a standard deviation of 0.9-in. Due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 3.3% or largest 3.3%.
What is the minimum head diameter that will fit the clientele?
min =
What is the maximum head diameter that will fit the clientele?
max =
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 by Boreal(15235) (Show Source): You can put this solution on YOUR website!
These sd s correspond to z's of -1.838 and +1.838 from the table.
z=(x-mean)/sd
1.838=(x-5.9)/0.9
1.654=x-5.9
x=7.554 in for largest size
x=4.246 in for smallest size
answer to 1 decimal place is (4.2 in, 7.6 in)
This is 0.9339 of the area of the normal curve taken out of the middle.
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