A survey is being planned to estimate, with a 98% confidence interval, the mean amount of time per week that seniors spend watching television. The population standard deviation is known to be 5.2 hours. What sample size will be required to obtain estimate that is within 0.5 hours of the population mean?
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The Solution provides the minimum required sample size.
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7.16 Daily output of Marathon's Garyville, Louisiana, refinery is normally distributed with a mean of
232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels. (a) What is the
probability of producing at least 232,000 barrels? (b) Between 232,000 and 239,000 barrels?
(c) Less than 239,000 barrels? (d) Less than 245,000 barrels? (e) More than 225,000 barrels?
7.17 Assume that the number of calories in a McDonald's Egg McMuffin is a normally distributed
random variable with a mean of 290 calories and a standard deviation of 14 calories. (a) What is
the probability that a particular serving contains fewer than 300 calories? (b) More than 250 calories?
(c) Between 275 and 310 calories? Show all work clearly. (Data are from McDonalds.com)
7.18 The weight of a miniature Tootsie Roll is normally distributed with a mean of 3.30 grams and
standard deviation of 0.13 grams. (a) Within what weight range will the middle 95 percent of all
miniature Tootsie Rolls fall? (b) What is the probability that a randomly chosen miniature
Tootsie Roll will weigh more than 3.50 grams? (Data are from a project by MBA student Henry
7.19 The time required to verify and fill a common prescription at a neighborhood pharmacy is normally
distributed with a mean of 10 minutes and a standard deviation of 3 minutes. Find the time
for each event. Show your work.
a. Highest 10 percent b. Highest 50 percent c. Highest 5 percent
d. Highest 80 percent e. Lowest 10 percent f. Middle 50 percent
g. Lowest 93 percent h. Middle 95 percent i. Lowest 7 percent
7.21 The weight of newborn babies in Foxboro Hospital is normally distributed with a mean of
6.9 pounds and a standard deviation of 1.2 pounds. (a) How unusual is a baby weighing
8.0 pounds or more? (b) What would be the 90th percentile for birth weight? (c) Within what
range would the middle 95 percent of birth weights lie?
8.6 Prof. Hardtack gave three exams last semester in a large lecture class. The standard deviation
Ï? = 7 was the same on all three exams, and scores were normally distributed. Below are scores
for 10 randomly chosen students on each exam. Find the 95 percent confidence interval for
the mean score on each exam. Do the confidence intervals overlap? If so, what does this suggest?
8.7 In a certain manufacturing process, the diameter of holes drilled in a steel plate is a normally
distributed random variable. The process standard deviation is known to be Ï?=0.005 cm.A sample
of 15 plates shows a mean hole diameter of 2.475 cm. Find the 95 percent confidence interval for ?.
8.11 A sample of 21 minivan electrical warranty repairs for loose, not attached wires (one of several
electrical failure categories the dealership mechanic can select) showed a mean repair cost of
$45.66 with a standard deviation of $27.79. (a) Construct a 95 percent confidence interval for the
true mean repair cost. (b) How could the confidence interval be made narrower? (Data are from a
project by MBA student Tim Polulak.)
8.13 A random sample of monthly rent paid by 12 college seniors living off campus gave the results
below (in dollars). Find a 99 percent confidence interval for ?, assuming that the sample is from
a normal population. Rents
900 810 770 860 850 790
810 800 890 720 910 640
8.19 From a list of stock mutual funds, 52 funds were selected at random. Of the funds chosen, it was
found that 19 required a minimum initial investment under $1,000. (a) Construct a 90 percent confidence
interval for the true proportion requiring an initial investment under $1,000. (b) May normality
be assumed? Explain.
8.22 A sample of 50 homes in a subdivision revealed that 24 were ranch style (as opposed to colonial,
tri-level, or Cape Cod). (a) Construct a 98 percent confidence interval for the true proportion of
ranch style homes. (b) Check the normality assumption.
8.27 Popcorn kernels are believed to take between 100 and 200 seconds to pop in a certain microwave.
What sample size (number of kernels) would be needed to estimate the true mean seconds to pop
with an error of ± 5 seconds and 95 percent confidence? Explain your assumption about Ï?.
8.28 Analysis showed that the mean arrival rate for vehicles at a certain Shell station on Friday afternoon
last year was 4.5 vehicles per minute. How large a sample would be needed to estimate this
yearâ??s mean arrival rate with 98 percent confidence and an error of ±0.5?
8.31 (a) What sample size would be needed to estimate the true proportion of American households
that own more than one DVD player, with 90 percent confidence and an error of ±0.02? (b) What
sampling method would you recommend? Why?
8.33 (a) What sample size would be needed to estimate the true proportion of American adults who
know their cholesterol level, using 95 percent confidence and an error of ±0.02? (b) What sampling
method would you recommend, and why?