# Project #33537 - Satistics- Normal Distribution

3.  Weights of newborn babies in the United States are normally distributed with a mean of 3420g and a standard deviation of 495g.

a) A newborn weighting less than 2200 is considered to be at risk because the mortality rate for the group is at least 1 %.   What percentage of the newborn babies are in the “at-risk” category?  If the ChicagoGeneralHospital has 900 births in a year, how many of those babies are in the at risk category?

b)  If the “at risk” category is redefined to be the lowest 2%, what is the weight cutoff separating at risk babied from those not at risk?

c) If 16 babies are randomly selected, find the probability that their mean weight is greater than 3700g.

d) If 49 newborn babies are randomly selected, find the probability that their mean weight is between 3300g and 3700g.

4.  The U.S. Marines Corps requires that men have heights between 64 in and 78 in.  The national Health survey shows that heights of men are normally distributed with a mean of  69.0 inches and a standard deviation of 2.8 inches.

a) Find the percentage of men meeting those heights requirements.  Are too many men denied the opportunity to join the Marines because they are too short or too tall? Explain your reasoning.

b)  If you are appointed to be the Secretary of Defense and you want to change the requirements so that only the shortest 2% and the tallest 2% are rejected, what are the new minimum and maximum height requirements?

c)  If 64 men are randomly selected, find the probability that their mean height is greater than 68.0 in.

5.   M&M plain candies have a mean weight of 0.9147 g and a standard deviation of 0.0369 g.

a)  Find the probability that a package will weight more than 0.9325 g.

b)   Find the probability that a package will weight between 0.8954 g and 0.9456g.

c)    What percentage of the packages weigh less than 0.8888g?

6.    Scores on the SAT Verbal test are normally distributed with a mean of 509 and a standard deviation of  112.

a)   What score will more than 20% of the student receive?

b) If a scholarship is offered for earning an 80% or better on the Sat Verbal, what score do you need to get the scholarship?

c) What score do you need to be in the 97% percentile?

d)   What is the score range where 68% of the scores will fall?

1.  Human body temperatures are normally distributed with a mean of 98.20 ° F and a standard deviations of 0.62° F.

a) BellveueHospital in New York City uses 100.6 F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever?  Does this percentage suggest that a cutoff of 100.6 F is appropriate?

b)  Physicians want to select a minimum temperature for requiring further medical tests.  What should that temperature be, if we want only 5.0% of healthy people to exceed it?

2. The length of pregnancies is normally distributed with a mean of 268 days and a standard deviation of 15 days.

a)  One classis use of the normal distribution  is inspired by a letter to Dear Abby” in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the Navy.  Given this information, find the probability of a pregnancy lasting 308 days or longer. What does this suggest?

b) If we stipulate that a baby is premature if the length of pregnancy is in the lowest 4%, find the length that separates premature babies from those who are not premature.

3.  The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on data from the College Board).  The College of Westport includes a minimum score of 1100 among its requirements.

a) What percentage of females does not satisfy that requirement?

b) If the requirement is changed to “a score that is in the top 40%” what is the minimum required score?  What is a practical difficulty that would be created if the new requirements were announced as the “top 40%”?

4.   Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years (based on data from “Getting Things Fixed”, Consumer Reports).

a) Find the probability that a randomly selected CD player will have a replacement time of less than 8.0 years.

b) If you want to provide a warranty so that only 2% of the CD players will be replaced before the warranty expires, what is the time length of the warranty?

Use the following information for problems 5-7.

The heights of women are normally distributed with a means of 63.6 inches and a standard deviation of 2.5 in.

5.  The Beanstalk Club, a social organization for tall people, has a requirement that women must be al least 5’ 11” tall.  What percentage of women meet that requirement?

6.  The U. S. army requires women’s heights to be between 4’10” and 6’ 8”.  Find the percentage of women meeting that height requirement.  Are too many women being denied the opportunity to join the Army because they are too short or too tall?

7.  In order to have a precision dance team with a uniform appearance, height restrictions are placed on the famous Rockette dancers at New York’s Radio City Music Hall.  Because women have grown taller, a more recent change now requires that a Rockette dancer must have a height between 66.5 in and 71.5 in.

a) What percentage of women meet this new height requirement?  Does it appear that Rockettes are generally taller than typical women?

b)  Suppose that those requirements must be changed because too few women now meet them.  What are the new minimum and maximum allowable heights if the shortest 20% and the tallest 20% are excluded?

 Subject Mathematics Due By (Pacific Time) 06/18/2014 04:00 pm
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