- The population mean annual salary for registered nurses is $59,100. A random sample of 35
registered nurses is selected from the population. What is the probability that the mean annual
salary of the sample is less than $55,000? Assume = $17,000. - The time that a technician requires to perform preventive maintenance on an air conditioning
unit is governed by an unknown distribution. The mean time is = 1 hour and the standard
deviation is = 1 hour. Your company operates 70 of these units. What is the probability that
their average maintenance exceeds 50 minutes?
1 - Days before the 1936 United States presidential election, Literary Digest, a reputable magazine
of the time, published a poll of 2,4000,000 respondents with the following results: 57% favored
Republican Alf Landon over Democrat Franklin Roosevelt. The poll involved contacting a total
of 10 million people by mail (using private clubs mailing lists or the telephone book). A Landon
victory was predicted and the prediction was o by 19% when Landon received only 38% of the
vote. Compare this 2,400,000 people poll to modern polls that typically sample from 1,000 to 1,500
people and claim to be accurate within 4% (if you have paid attention to Gallup, Harris, and other
reputable pollsters in recent years, there is no reason to disagree with their claim). Why was it
that the Literary Digest poll couldn’t do nearly as well with a much larger sample? - Mr. V has nished grading and recording all of the scores for a dicult exam. Here are the
scores: 53, 94, 90, 77, 83, 98, 75, 82, 94, 79, 71, 76, 90, 87, 71, 72, 71, 86, 96, 94, 82, 70, 81, 88,
84, 91, 90, 90, 90, 65, 100, 89. He now needs to arrange the scores to determine whether the exam
should be curved. In order to do this, he constructs a stem-and-leaf plot.
2 - You work for a consumer advocate agency and want to nd the mean repair cost of a washing
machine. As part of your study, you randomly select 40 repair costs and nd the mean to be
$120:00. Construct a 96% con dence interval for the population mean repair cost. Assume =
$17:50. - Large trees growing near power lines can cause power failures during storms when their branches
fall on the lines. Power companies spend a great deal of time and money trimming and removing
trees to prevent this problem. Researchers are developing hormone and chemical treatments that
will stunt or slow tree growth. If the treatment is too severe, however, the tree will die. In one
series of laboratory experiments on 216 sycamore trees, 41 trees died. Give a 99% con dence
interval for the proportion of sycamore trees that would be expected to die from this particular
treatment.
3 - In 1998, a Sports Clinic in Cupertino, California, sent a mailing to all registered triathletes
in the United States. The mailing consisted of a questionnaire inquiring about injuries incurred
during training. Out of the 400 triathletes who responded, 160 said they had su ered some sort
of training related injury during the previous twelve months. Let p = the proportion of triathletes
who su ered a training related injury during the past year.Find the 90% con dence interval for p. - It is known that the number of pizza slices the average college student in America eats per
week is 10. Let’s suppose we wanted to determine if the average student at De Anza eats more
pizza than the average American college student. In order to do this, we take a random sample of
100 students. For the students in the sample, the average number of pizza slices is 10.2. At the
0.10 signi cance level, does the average De Anza College student eat more pizza than the average
American student? (Let’s suppose we know that the standard deviation for the number of pizza
slices for De Anza College students is 5.)
4 - In your work for a national health organization, you are asked to monitor the amount of sodium
in a certain brand of cereal. You nd that a random sample of 52 cereal servings has a mean sodium
content of 232 milligrams. At = 0.04, can you conclude that the mean sodium content per serving
of cereal is greater than 230 milligrams? Assume = 10 milligrams. - Do middle-aged male executives have di erent average blood pressure than the general population? The National Center for Health Statistics reports that the mean systolic blood pressure
for males 35 to 44 years of age is 128. The medical director of a company looks at the medical
records of 72 company executives in this age group (chosen at random) and nds that the mean
systolic blood pressure in this sample is x = 126.07. Is this enough evidence that executive blood
pressures di er from the national average? Assume that the standard deviation for all middle aged
executives is 15.
Sample Solution
