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 6.2-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 3% or largest 3%.What is the minimum head breadth that will fit the clientele?min =What is the maximum head breadth that will fit the clientele?min =Enter your answer as a number accurate to 1 decimal place. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

2.The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.916 g and a standard deviation of 0.302 g. Find the probability of randomly selecting a cigarette with 0.312 g of nicotineor less.

P(

X

< 0.312 g) =

Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact

z

-scores or

z

-scores rounded to 3 decimal places are accepted.

3.A distribution of values is normal with a mean of 149.3 and a standard deviation of 59.6.