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In: Statistics and Probability

Lunch break: In a recent survey of 655 working Americans ages 25|34, the average weekly amount...

Lunch break: In a recent survey of 655 working Americans ages 25|34, the average weekly
amount spent on lunch was $44.60 with standard deviation $2.81. The weekly amounts are approx-
imately bell-shaped.


(a) Estimate the percentage of amounts that are between $36.17 and $53.03.
(b) Estimate the percentage of amounts that are between $41.79 and $47.41.
(c) Between what two values will approximately 95% of the amounts be?


2. Pay your bills: In a large sample of customer accounts, a utility company determined that
the average number of days between when a bill was sent out and when the payment was made is
32 with a standard deviation of 7 days. Assume the data to be approximately bell-shaped.


(a) Between what two values will approximately 68% of the numbers of days be?
(b) Estimate the percentage of customer accounts for which the number of days is between 18 and
46.
(c) Estimate the percentage of customer accounts for which the number of days is between 11 and 53.


3. Precision manufacturing: A process manufactures ball bearings with diameters that are
normally distributed with mean 25.1 millimeters and standard deviation 0.08 millimeter.
(a) What proportion of the diameters are less than 25.0 millimeters?
(b) What proportion of the diameters are greater than 25.4 millimeters?
(c) To meet a certain specication, a ball bearing must have a diameter between 25.0 and 25.3
millimeters. What proportion of the ball bearings meet the specication?


4. Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year xed
rate mortgage from a sample of lenders in Macon, Georgia on June 20, 2013. It is reasonable to
assume that the population is approximately normal.
4.75 4.375 4.176 4.679 4.426 4.227 4.125 4.250 3.950 4.191 4.299 4.415
Source: www.bankrate.com
Construct a 99% condence interval for the mean rate and interpret it.
One week earlier, the mean rate was 4.050%. A mortgage broker claims that the mean rate is
now higher. Based on the condence interval, is this a reasonable claim? Explain.


5. How smart is your phone? A random sample of 11 Samsung Galaxy smartphones being sold
over the Internet in 2013 had the following prices, in dollars:
199 169 385 329 269 149 135 249 349 299 249
Assume the population standard deviation = 85. Assuming that the population is approx-
imately normal, construct a 95% condence interval for the mean price for all phones of this type
being sold on the Internet in 2013.


6. Big salary for the boss: Following is the total 2012 compensation, in millions of dollars,
for Chief Executive Ocers at 20 large U.S. corporations.
2.75 9.15 2.32 23.84 13.12 9.91 6.29 2.19 4.28 0.70
3.18 8.20 1.68 4.64 6.05 6.59 11.31 1.35 25.84 2.85

Assuming that the conditions for constructing a condence interval for the mean compensation
are satised, construct and interpret a 95% condence interval for the mean compensation of a
Chief Executive Ocer.

In 2011, the average total compensation, in millions of dollars, for Chief Executive Ocers at
these corporations was 11.41. An analyst claims that the mean compensation has decreased in
2012. Does your condence interval support the analyst's claim? Explain.


7. Working at home: According to the U.S. Census Bureau, 43% of men who worked at
home were college graduates. In a sample of 500 women who worked at home, 162 were college
graduates.

Find a point estimate for the proportion of college graduates among women who work
at home. Construct a 98% condence interval for the proportion of women who work at home who
are college graduates.


Based on the condence interval, is it reasonable to believe that the proportion of college graduates
among women who work at home is the same as the proportion of college graduates among men
who work at home? Explain.


8. Internet service: An Internet service provider sampled 540 customers and found that 75
of them experienced an interruption in high-speed service during the previous month.

Find a point
estimate for the population proportion of all customers who experienced an interruption. Construct
a 90% condence interval for the proportion of all customers who experienced an interruption.


The company's quality control manager claims that no more than 10% of its customers expe-
rienced an interruption during the previous month. Does the condence interval contradict this
claim? Explain.

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Expert Solution

orchestra answered 2 years ago
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