Download Statistics 101 – Homework 6

Statistics 101 – Homework 6
Due Friday, October 21, 2005
Homework is due on the due date at the end of the lecture.
Reading:
October 12 – October 19
October 21 – October 26
Chapter 18 (p. 406–412 )
Chapter 19
Assignment:
1. The maker of M&M’s says on its website that 20% of Almond M&M’s are
yellow. Suppose that M&M’s are packaged at random. We wish to examine the
sample proportion of yellow M&M’s, p̂ , in various sized bags.
a) For each of the different sized bags, give the mean and standard deviation
of the sampling distribution of p̂ . Also comment on whether or not the
conditions are met for the sampling distribution to be approximately
normal.
i) Fun size bags containing 25 M&M’s.
ii) Small bags containing 50 M&M’s
iii) Large bags containing 200 M&M’s
iv) Extra large bags containing 400 M&M’s
b) For the extra large bags containing 400 M&M’s, use the 68-95-99.7 Rule
to describe how the sample proportion of yellow M&M’s might vary from
bag to bag.
c) In an extra large bag of 400 M&M’s there are only 52 yellow M&M’s. Is
this an unusually small number of yellow M&M’s? Explain.
2. For colleges and universities in the U.S., the freshman-to-sophomore retention
rate is 74% (that is, 74% of freshmen return for their sophomore year). Consider
colleges and universities that have freshman classes of 1000 students. Use the 6895-99.7 Rule to describe the sampling distribution model for the proportion of
those freshmen we expect to return for their sophomore year. Are the appropriate
conditions met? Explain.
3. A national survey found that 44% of college students engage in binge drinking (5
or more drinks at a sitting for men, 4 or more for women). Use the 68-95-99.7
Rule to describe the sampling distribution model for the proportion of students in
a randomly selected group of 100 college students who engage in binge drinking.
Do you think that the appropriate conditions are met? Explain.
4. When a truckload of apples arrives at a packaging facility, a random sample of
200 apples is selected and examined for bruises, discoloration and other defects.
The whole truckload will be rejected if more than 5% of the sample is
unsatisfactory due to defects. Suppose that actually 8% of the apples on the truck
are unsatisfactory. What is the probability that the truckload will be accepted
anyway? Do you think that the appropriate conditions for computing this
probability are met? Explain.