1) Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data point between z=-1.8 and z= 1.8 standard deviations of the mean ( or within 1.8 standard deviations of the mean) what percent of the data points will fall in that range. Answer ( Enter a number between 0 and 100 , not 0 and 1 and round to 2 decimal places.

2)Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0 degree Celsius and a standard deviation of 1.00 degree Celsius. A single thermometer is randomly selected and tested. Find P94 , the 94 percentile. This is the temperature reading separating the bottom 94% from the top 6%.

3)The scores on a standardized test are normally distributed with a mean of 95 and a standard deviation of 20 , what test score is 0.6 standard deviations above the mean?

4)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 6.1 -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 1.3% or largest 1.3%.

a)what is the minimum head breadth that will fit the clientele?

b)what is the maximum head breadth that will fit the clientele?

5)if P( 0 < z < a )=0.2257 , find a.

6)if P( -0.5 < z < b)=0.6766 , find b

7)Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0 degree Celsius and a standard deviation of 1.00 degree Celsius. A single thermometer is randomly selected and tested. If 1.1% of the thermometers are rejected because they have readings that are too high and another 1.1% are rejected because they have readings that are too low , find the two readings that are cutoff values separating the rejected thermometers from the others.( round your answers to three decimal places when needed) Interval of acceptable thermometer readings =