1. Assume the following data were gathered by a manufacturer of a robotics component, in
units of days of continuous use until the component fails. There are 60
measurements in this data set. Show a histogram of this data set with 10 bins
of equal size, spanning the range from the data minimum to the data maximum.
142, 147, 127, 161, 145, 137, 122, 123, 141, 139, 139
135, 135, 130, 147, 118, 154, 133, 136, 129, 139, 131
143, 130, 160, 127, 127, 145, 144, 155, 128, 124,144
133, 136, 133, 151, 131, 133, 119, 122, 139, 128, 121
142, 136, 148, 136, 121, 131, 125, 120, 123, 145, 140
150, 136, 135, 133, 134
2. A university has been tracking the percentage of alumni giving to its annual fund
each year for the past 10 years. The data is given here.
14%, 13%, 15%, 21%, 19%, 24%, 25%, 28%, 25%. 31%
Answer the following questions about this data.
a.what are its mean and median?
b.What is the procedure for using mean and median to determine whether the data
is skewed, and if so, in what direction?
c.Apply the procedure you described to the mean and median computed in part a.
3. Assume you have a data set from a normally distributed random variable. Answer the
following questions about it.
a.Will the random variable be discrete, continuous, or neither? How do you
b. Will the data be qualitative or quantitative? How do you know?
4. A nurse is considering going back to graduate school to earn a Ph.D. in
biochemistry. One of the schools she visits tells her that the average time to
earn the degree she’s considering is 5.5 years. Show that this statement is not
sufficiently precise by giving two different explanations of what it might
5. Under which of the following conditions would it be appropriate to use a Binomial
random variable? In each case, explain why your answer is correct.
a. A department will interview 10 candidates for a position, and call back for
second interviews those who answer the interview questions to the satisfaction
of all the interviewers. They hope to call back at least 3, but past experience
suggests an average of about 1 call back per 4 interviews.
b. A factory posts on the wall the number of days since its last safety
infraction of injury. In the past year, the factory has had a safety infraction
or injury on 6 different days. The factory is interested in the n umber of days
that can be expected to elapse without an injury.
c. Fifteen of a doctor’s patients have the same ailment. Studies have shown
that about 86.5% of patients with this ailment respond to a certain drug. The
doctor prescribes the drug to all 15, but the number who will respond in this
case is, of course, not known in advance.
6. The mean time for a racecar driver’s crew to perform a pit stop is 13.2 seconds,
with a standard deviation of 0.9 seconds. To maintain his current lead, the
driver needs a pit stop in 12.5 seconds or less. Assuming this random variable
is normally distributed, what is the probability of the driver getting the pit
stop in a short enough time to maintain is lead?
7. From a sample of size 175, the sample mean is x bar=54.37 and sample standard
deviation is s= 7.07.
a. Construct a 95% confidence interval for the population mean and show your
b. Explain how your work in part a would have been different if the sample size
had been only 12 instead.
8. A random sample from the population of registered voters in California is to be
taken and then surveyed about an upcoming election. What sample size should be
used to guarantee a sampling error of 3% or less when estimating p at the