1.A distribution of values is normal with a mean of 141.1 and a standard deviation of 20.7.

FindP₆₀, which is the score separating the bottom 60% from the top 40%.

P₆₀=___________

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.Company XYZ know that replacement times for the DVD players it produces are normally distributed with a mean of 8.4 years and a standard deviation of 1 years.

Find the probability that a randomly selected DVD player will have a replacement time less than 5.2 years?

P(X< 5.2 years) =_________

Enter your answer accurate to 4 decimal places. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

If the company wants to provide a warranty so that only 3.9% of the DVD players 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. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

3.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 6.4-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 2.2% or largest 2.2%.

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 exactz-scores orz-scores rounded to 3 decimal places are accepted.

4.A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admittance. Scores on the SAT test are normally distributed with a mean of 993 and a standard deviation of 195. Scores on the ACT test are normally distributed with a mean of 22.4 and a standard deviation of 4.2. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 69-percentile, find the actual SAT score.

SAT score =

Round answer to a whole number.

What would be the equivalent ACT score for this student?

ACT score =

Round answer to a whole number.

If a student gets an SAT score of 1403, find the equivalent ACT score.

ACT score =

Round answer to a whole number.

Using all 1991 birth records in the computerized national birth certificate registry compiled by the National Center for Health Statistics (NCHS), statisticians Traci Clemons and Marcello Pagano found that the birth weights of babies in the United States are not symmetric ("Are babies normal?"The American Statistician, Nov 1999, 53:4). However, they also found that when1.infants born outside of the "typical" 37-43 weeks and infants born to mothers with a history of diabetes are excluded, the birth weights of the remaining infants do follow a Normal model with mean = 3432 g and standard deviation = 482 g. The following questions refer to infants born from 37 to 43 weeks whose mothers did not have a history of diabetes.

Compute thez-score of an infant who weighs 3641 g. (Round your answer to two decimal places.) _________________

Approximately what fraction of infants would you expect to have birth weights between 2720 g and 4320 g? (Express your answer as a decimal, not a percent, and round to three decimal places.) __________________

Approximately what fraction of infants would you expect to have birth weights below 2720 g? (Express your answer as a decimal, not a percent, and round to three decimal places.) ___________________

A medical researcher wishes to study infants with high birth weights and seeks infants with birth weights among the heaviest 13%. Above what weight must an infant's birth weight be in order for the infant be included in the study? (Round your answer to the nearest gram.) ___________________g