Project #10145 - Introduction to Statistics

1. Consider the following five outcomes for an experiment in which the type of ice cream purchased by the next customer at a certain store is noted.

 Brand Steve's Ben & Jerry's Breyer's Breyer's Von's Size of Container Pint Pint Quart Half Gal Half Gal Probability .10 .15 .20 .25 .30

a. Is this a probability distribution? Why or why not?
b. What is the probability that Breyer's ice cream is purchased?
c. What is the probability that Von's brand is not purchased?
d. What is the probability that the size is purchased is larger than a pint?

2. Five hundred first-year students at a state university were classified both according to high school GPA and whether or not they were on academic probation at the end of their first semester.

 High School GPA Probation 2.5 - <3.0 3.0 - <3.5 3.5 and above Total Yes 50 55 30 135 No 45 135 185 365 Total 95 190 215 500

a. Use the table to determine the probability that a randomly selected first-year student will be on academic probation at the end of the first semester.

b. What is the probability that a randomly selected first-year student had a GPA of 3.5 or above?

c. Are the outcomes selected student has a GPA of 3.5 or above and selected student is on academic probation at the end of first semester independent? How can you tell?

d. What is the probability that a first-year student will have a high school GPA of between 2.5 and 3.0 and will also be on academic probation at the end of the first semester of college?

e. What is the probability that a first year student will have a high school GPA of 3.5 or above and will not be on probation at the end of first semester of college?

3. An issue of Scientific American reveals that the batting averages of major league players are approximately normally distributed and have a mean of 0.270 and a standard deviation of 0.031. Determine the percentage of major league baseball players having batting averages:

a. Between 0.225 and 0.250.

b. At least 0.300.

c. At most 0.280

4. Suppose that the mean value of interpupillary distance for all adult males is 65 mm, and the population standard deviation is 5 mm.

a. If the distribution of interpupillary distance is normal and a sample of n = 25 adult males is selected, what is the probability that the mean distance for the sample will be between 64 and 67?   At least 68mm?

b. Suppose that a random sample of 100 males is obtained. What is the probability that the mean distance for the sample will be between 64 and 67? At least 68mm?

5.  The U.S. Bureau of the Census reported in Current Housing Reports that the mean livable square footage for single-family detached homes is 1742 square feet with a standard deviation of 560 sq. ft.

a. For random samples of 25 single-family detached homes, determine the mean and standard deviation of the distribution of the mean square footages of the homes.

b. For random samples of 25 single-family detached homes, determine the probability that the mean square footage is between 1630 sq. ft. and 1854 sq. ft.

c. Suppose that random samples of 400 single-family detached homes are obtained. Determine the mean and standard deviation of the distribution of the mean square footages of the homes.

d.  For random samples of 400 single-family detached homes, determine the probability that the mean square footage is between 1630 sq. ft. and 1854 sq. ft.

e.  For random samples of 400 single-family detached homes, determine the probability that the mean square footage is less than 1742 sq. ft.

 Subject Mathematics Due By (Pacific Time) 08/01/2013 04:00 pm
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