STATISTICS 101 - Homework 6a
Due Monday, March 11, 2002
• Homework is due by the end of class on the due date.
• You may talk with others about the homework problems but please write your solutions up
independently.
• Please answer homework questions in complete sentences. Make sure to staple the pages of
your assignment together. Be sure to indicate your lab section on your paper.
• You will have an opportunity to get help on homework during lab.
Reading:
Mar. 1
- Mar. 6
Section 4.3
Assignment:
1. Read pages 236-248 and do exercises 4.42 and 4.44 in the text.
2. During a day, a diet conscious individual consumes food that has a total caloric content, X,
that is normally distributed with mean, µ = 1850 calories and standard deviation, σ = 120
calories.
(a) For a single day, chosen at random, what is the probability that the food consumed by
this individual will contain more than 2000 calories?
(b) For a random sample of 25 days, describe the sampling dilatstribution of X, the sample
mean caloric content of food consumed. Does this result depend on the Central Limit
Theorem? Explain briefly.
(c) What is the chance that the sample mean caloric content of food consumed for a random
sample of 25 days will be less than 1775 calories?
3. Large packages of potato chips are supposed to contain 13 ounces of product. When the
filling process is working correctly the actual weight of contents is approximately normally
distributed with mean µ=13.6 ounces and standard deviation σ=0.5 ounces. The mean is set
high so that the under-filling will not occur frequently.
(a) Find the probability that a randomly selected package contains less than 13 ounces.
(b) As part of a quality control effort, the company takes a random sample of 16 packages
each day and weighs the contents of each. Find the probability that the sample mean
weight for the 16 packages is less than 13 ounces. Explain why the answer here is so
much smaller than in part (a).
(c) The company will not ship the days production if the sample mean weight of the 16
packages is too low. What should the cut off value be so that the chance of not shipping
the days production is 0.01?
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