Question

1.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 7-in and a standard deviation of 1.2-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 = What is the maximum head breadth that will fit the clientele? max = Enter your answer as a number accurate to 1 decimal place.

2.Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 16.9 years and a standard deviation of 1.8 years.

Find the probability that a randomly selected quartz time piece will have a replacement time less than 11.9 years?
P(X < 11.9 years) =

Enter your answer accurate to 4 decimal places.

If the company wants to provide a warranty so that only 2.5% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?
warranty =  years

Enter your answer as a number accurate to 1 decimal place.

Answer 1

1)

for 1.2 % end values , critical z =-2.26

minimum head breadth that will fit the clientele =7-2.26*1.2 =4.3

maximum head breadth that will fit the clientele =7+2.26*1.2 =9.7

2)

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	16.9
std deviation   =σ=	1.8

probability =P(X<11.9)=(Z<(11.9-16.9)/1.8)=P(Z<-2.78)=0.0027

b)

for 5th percentile critical value of z=		-1.645
therefore corresponding value=mean+z*std deviation=			13.9