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 6.4-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 breadths that are in the smallest 1.1% or largest 1.1%. What is the minimum head breadth that will fit the clientele? min = What is the maximum head breadth 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.
Solution:-
Given that,
mean = = 6.4
standard deviation = = 0.9
Using standard normal table,
P(Z < z) = 1.1%
= P(Z < z ) = 0.011
= P(Z < -2.290 ) = 0.011
z = - 2.290
Using z-score formula,
x = z * +
x = - 2.290 * 0.9 + 6.4
x = 4.3
minimum = 4.3
Using standard normal table,
P(Z > z) = 1.1%
= 1 - P(Z < z) = 0.011
= P(Z < z) = 1 - 0.011
= P(Z < z ) = 0.989
= P(Z < 2.290 ) = 0.89
z = 2.290
Using z-score formula,
x = z * +
x = 2.290 * 0.9 + 6.4
x = 8.5
maximum = 8.5
Get Answers For Free
Most questions answered within 1 hours.