Math 15
Assessment # 2
1. Given the following frequency distribution that indicates the number of cats per household.
CATS HOUSEHOLDS
0273
1349
2203
3 78
4 57
5 40.
a)Use this frequency distribution to construct a probability distribution.
b)Find the mean.
c)Find the standard deviation.
2. For each situation, indicate whether the random variable would follow a Discrete or Continuousdistribution.
a)X = the volume of monkey brain in cubic centimeters.
b)X = the number of draws it takes to draw a king.
c)X = the times it takes a plumber to fix a toilet.
d)X = the number of cars in a parking lot.
3. Fifty four percent of men consider themselves basketball fans. You randomly select 10 men and ask each if he considers himself a basketball fan. Find the probability that the number who consider themselves basketball fan is
a)Exactly eight
b)At least eight.
c)Less than eight.
4. Volumes of standard size cans of Inka Kola follow a normal distribution with mean ounces and standard deviation ounces.
Compute the z-scores for each of the following readings.
a)x = 17.00 ounces
b)x = 15.50 ounces
c)x = 16.75 ounces.
d)x = 14.45 ounces.
5. It is reported that the cholesterol level for U. S. women ages between 50 and 59 yields a mean milligrams per deciliter and a standard deviation milligrams per deciliter. (Assume the distribution is Normally Distributed)
a)What percentage of women has a total cholesterol level less than 239 milligrams per deciliter of blood?
b)If 200 U. S. women in the 50-59 age group were randomly selected, about how many would you expect to have a total cholesterol level greater than 200 milligrams per deciliter of blood?
6. The lifespan of wood flies follows a normal distribution with mean hours, and standard deviation hours.
a)What lifespan would be the cut-off (to the nearest tenth of an hour) to be in the top 10%?
b)What life span would be the cut-off (to the nearest tenth of an hour) to be in the bottom 15%?
7. The yearly grain consumption of a Wool sheep has a mean pounds and standard deviation pounds.
a)If a sample of 100 sheep is taken, then, the average of the grain consumptions follows an approximate normal distribution. Find the mean and standard deviation.
b)What is the probability that, from the sample of 100 sheep, the average exceeds 1828 pounds?
8. The NSSL in Oklahoma has determined that the probability a tornado will occur in the state, in a day, is 22%. Compute the following probabilities.
a)Out of 90 observed days, 25 or more tornados occur in the state.
b)Out of 90 days observed, fewer than fifteen tornados occur in the state.
9. The U.S. Department of health and Human Services reports that there were 250,000 babies born to teenagers 15-18 in 2004.
AGE NUMBER OF BABIES
15 17,500
16 42,500
17 72,500
18 117,500
a) Construct a Probability Distribution
b) Find the mean and standard deviation.
10. Give two examples each of discrete random variables, and continuous random variables.
11. Ten percent of people are left-handed. If 15 students are enrolled in a History Honors class,
a) What is the probability that exactly 6 of the students are left-handed?
b) The probability that at least one of them is left handed?
c) The probability that more than 13 are left handed?
12. Several students are unprepared for a multiple-choice Math quiz with 10 questions, and all of their answers are guesses. Each question has 5 possible answers, but only one is correct.
a)Does this procedure results in a Binomial Distribution? If yes, identify all requirements needed for this particular procedure.
b)Find the mean and standard deviation.
c)Use part b) to indicate whether is usual or unusual for a student to score by guessing at least 6 correct answers? Explain why or why not.
13. Mens heights are normally distributed with mean and standard deviation Find the z-scores for the following values:
a) b)
14. The World Health Organization states that tobacco is the second cause of death in the world. Every year a mean of 5 million people die of tobacco-related causes. Find the probability that more than 4 million people will die of tobacco-related causes in any particular year
(Tobacco-related deaths are normally distributed with and)
15. The state of Georgia reports that the average temperature statewide for the month of April from 1949 to 2010 was with Standard Deviation . Temperature readings are Normally Distributed.
a) What is the probability that any given day, during this given time that the temperature was between
b) What is the probability that any given day, during this given time that the temperature was
greater than
16. Scores for an entry exam to a university are normally distributed with a mean of 72 and a standard deviation of 3.8.
a) If the top 15% are admitted with a full scholarship, what is the lowest score a student can obtain to earn a full scholarship?
b) The university decides that students, who score below or at the 20th percentile, must take remedial courses. If a student scores 60 on the entry exam, will he/she be taking remedial courses? Explain why.
17. Suppose that statistics quiz scores for a certain instructor are normally distributed with a mean 70 and standard deviation 10. Suppose that over the years the instructor has had many sections of size
a) If 25 students are randomly selected, find the sample mean and the sample standard deviation for the sampling distribution of .
b) Find the probability that a sample of 25 quiz scores will have a mean score greater than 73.5
18. It is known that 64% of Americans would favor an increased federal tax on gasoline. For a sample of 200 Americans, what is the probability that at least 138 Americans would favor such a tax?
