Mesa Verde Museum Association). Suppose a doe that weighs less than 54 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (b) If the park has about 2200 does, what number do you expect to be under- nourished in December? (c) Interpretation To estimate the health of the December doe population, park rangers use the rule that the average weight of n = be more than 60 kg. If the average weight is less than 60 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample less than 60 kg (assume a healthy population)? (d) Interpretation Compute the probability that i< 64.2 kg for 50 does (assume a healthy population). Suppose park rangers captured, weighed, and released 50 does in December, and the average weight was 64.2 kg. Do you think the doe population is undernourished or not? Explain. 50 does should 50 does is

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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(c) Interpretation Suppose the weight of coal in one car was less than
74.5 tons. Would that fact make you suspect that the loader had slipped
out of adjustment? Suppose the weight of coal in 20 cars selected at ran-
dom had an average x of less than 74.5 tons. Would that fact make you
suspect that the loader had slipped out of adjustment? Why?
14.| Vital Statistics: Heights of Men The heights of 18-year-old men are ap-
proximately normally distributed, with mean 68 inches and standard devia-
tion 3 inches (based on information from Statistical Abstract of the United
States, 112th edition).
(a) What is the probability that an 18-year-old man selected at random is
between 67 and 69 inches tall?
(b) If a random sample of nine 18-year-old men is selected, what is the
probability that the mean height x is between 67 and 69 inches?
(c) Interpretation Compare your answers to parts (a) and (b). Is the prob-
ability in part (b) much higher? Why would you expect this?
15.| Medical: Blood Glucose Let x be a random variable that represents the level
of glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast.
Assume that for people under 50 years old, x has a distribution that is approx-
imately normal, with mean µ
(based on information from Diagnostic Tests with Nursing Applications,
edited by S. Loeb, Springhouse). A test result x < 40 is an indication of
severe excess insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test, x < 40?
(b) Suppose a doctor uses the average x for two tests taken about a week
apart. What can we say about the probability distribution of x? Hint: See
Theorem 6.1. What is the probability that x < 40?
(c) Repeat part (b) for n
(d) Repeat part (b) for n =
(e) Interpretation Compare your answers to parts (a), (b), (c), and (d). Did
the probabilities decrease as n increased? Explain what this might imply
if you were a doctor or a nurse. If a patient had a test result of x < 40
based on five tests, explain why either you are looking at an extremely
rare event or (more likely) the person has a case of excess insulin.
85 and estimated standard deviation o =
25
3 tests taken a week apart.
5 tests taken a week apart.
16.| Medical: White Blood Cells Let x be a random variable that represents
white blood cell count per cubic milliliter of whole blood. Assume that x
has a distribution that is approximately normal, with mean u =
7500 and
estimated standard deviation o =
1750 (see reference in Problem 15). A test
result of x < 3500 is an indication of leukopenia. This indicates bone mar-
row depression that may be the result of a viral infection.
(a) What is the probability that, on a single test, x is less than 3500?
(b) Suppose a doctor uses the average i for two tests taken about a week
apart. What can we say about the probability distribution of x? What is
the probability of x < 3500?
(c) Repeat part (b) for n
(d) Interpretation Compare your answers to parts (a), (b), and (c). How did
the probabilities change as n increased? If a person had x < 3500 based
on three tests, what conclusion would you draw as a doctor or a nurse?
3 tests taken a week apart.
17.| Wildlife: Deer Let x be a random variable that represents the weights in
kilograms (kg) of healthy adult female deer (does) in December in Mesa
Verde National Park. Then x has a distribution that is approximately normal,
with mean u
63.0 kg and standard deviation o
7.1 kg (Source: The
Mule Deer of Mesa Verde National Park, by G. W. Mierau and J. L. Schmidt,
jhts Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208
Transcribed Image Text:(c) Interpretation Suppose the weight of coal in one car was less than 74.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Suppose the weight of coal in 20 cars selected at ran- dom had an average x of less than 74.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? 14.| Vital Statistics: Heights of Men The heights of 18-year-old men are ap- proximately normally distributed, with mean 68 inches and standard devia- tion 3 inches (based on information from Statistical Abstract of the United States, 112th edition). (a) What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? (b) If a random sample of nine 18-year-old men is selected, what is the probability that the mean height x is between 67 and 69 inches? (c) Interpretation Compare your answers to parts (a) and (b). Is the prob- ability in part (b) much higher? Why would you expect this? 15.| Medical: Blood Glucose Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast. Assume that for people under 50 years old, x has a distribution that is approx- imately normal, with mean µ (based on information from Diagnostic Tests with Nursing Applications, edited by S. Loeb, Springhouse). A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed. (a) What is the probability that, on a single test, x < 40? (b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1. What is the probability that x < 40? (c) Repeat part (b) for n (d) Repeat part (b) for n = (e) Interpretation Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? Explain what this might imply if you were a doctor or a nurse. If a patient had a test result of x < 40 based on five tests, explain why either you are looking at an extremely rare event or (more likely) the person has a case of excess insulin. 85 and estimated standard deviation o = 25 3 tests taken a week apart. 5 tests taken a week apart. 16.| Medical: White Blood Cells Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean u = 7500 and estimated standard deviation o = 1750 (see reference in Problem 15). A test result of x < 3500 is an indication of leukopenia. This indicates bone mar- row depression that may be the result of a viral infection. (a) What is the probability that, on a single test, x is less than 3500? (b) Suppose a doctor uses the average i for two tests taken about a week apart. What can we say about the probability distribution of x? What is the probability of x < 3500? (c) Repeat part (b) for n (d) Interpretation Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased? If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse? 3 tests taken a week apart. 17.| Wildlife: Deer Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in Mesa Verde National Park. Then x has a distribution that is approximately normal, with mean u 63.0 kg and standard deviation o 7.1 kg (Source: The Mule Deer of Mesa Verde National Park, by G. W. Mierau and J. L. Schmidt, jhts Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208
PLING DISTRIBUTIONS
Mesa Verde Museum Association). Suppose a doe that weighs less than 54 kg
is considered undernourished.
(a) What is the probability that a single doe captured (weighed and released)
at random in December is undernourished?
(b) If the park has about 2200 does, what number do you expect to be under-
nourished in December?
(c) Interpretation To estimate the health of the December doe population,
park rangers use the rule that the average weight of n
be more than 60 kg. If the average weight is less than 60 kg, it is thought
that the entire population of does might be undernourished. What is the
probability that the average weight i for a random sample of 50 does is
less than 60 kg (assume a healthy population)?
(d) Interpretation Compute the probability that i < 64.2 kg for 50
does (assume a healthy population). Suppose park rangers captured,
weighed, and released 50 does in December, and the average weight was
x = 64.2 kg. Do you think the doe population is undernourished or not?
Explain.
50 does should
Focus Problem: Impulse Buying Let x represent the dollar amount spent on
supermarket impulse buying in a 10-minute (unplanned) shopping interval.
Based on a Denver Post article, the mean of the x distribution is about $20
and the estimated standard deviation is about $7.
(a) Consider a random sample of n
10 minutes of unplanned shopping time in a supermarket. From the central
limit theorem, what can you say about the probability distribution of x,
the average amount spent by these customers due to impulse buying?
What are the mean and standard deviation of the x distribution? Is it
necessary to make any assumption about the x distribution? Explain.
(b) What is the probability that x is between $18 and $22?
(c) Let us assume that x has a distribution that is approximately normal.
What is the probability that x is between $18 and $22?
(d) Interpretation: In part (b), we used x, the average amount spent, com-
puted for 100 customers. In part (c), we used x, the amount spent by only
one customer. The answers to parts (b) and (c) are very different. Why
would this happen? In this example, x is a much more predictable or reli-
able statistic than x. Consider that almost all marketing strategies and
sales pitches are designed for the average customer and not the individual
customer. How does the central limit theorem tell us that the average cus-
100 customers, each of whom has
tomer is much more predictable than the individual customer?
Finance: Templeton Funds Templeton World is a mutual fund that invests
in both U.S. and foreign markets. Let x be a random variable that represents
the monthly percentage return for the Templeton World fund. Based on
information from the Morningstar Guide to Mutual Funds (available in most
libraries), x has mean µ
1.6% and standard deviation o =
0.9%.
(a) Templeton World fund has over 250 stocks that combine together to give
the overall monthly percentage return x. We can consider the monthly
return of the stocks in the fund to be a sample from the population of
monthly returns of all world stocks. Then we see that the overall monthly
Transcribed Image Text:PLING DISTRIBUTIONS Mesa Verde Museum Association). Suppose a doe that weighs less than 54 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (b) If the park has about 2200 does, what number do you expect to be under- nourished in December? (c) Interpretation To estimate the health of the December doe population, park rangers use the rule that the average weight of n be more than 60 kg. If the average weight is less than 60 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight i for a random sample of 50 does is less than 60 kg (assume a healthy population)? (d) Interpretation Compute the probability that i < 64.2 kg for 50 does (assume a healthy population). Suppose park rangers captured, weighed, and released 50 does in December, and the average weight was x = 64.2 kg. Do you think the doe population is undernourished or not? Explain. 50 does should Focus Problem: Impulse Buying Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a Denver Post article, the mean of the x distribution is about $20 and the estimated standard deviation is about $7. (a) Consider a random sample of n 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution? Is it necessary to make any assumption about the x distribution? Explain. (b) What is the probability that x is between $18 and $22? (c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $18 and $22? (d) Interpretation: In part (b), we used x, the average amount spent, com- puted for 100 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen? In this example, x is a much more predictable or reli- able statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average cus- 100 customers, each of whom has tomer is much more predictable than the individual customer? Finance: Templeton Funds Templeton World is a mutual fund that invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the Templeton World fund. Based on information from the Morningstar Guide to Mutual Funds (available in most libraries), x has mean µ 1.6% and standard deviation o = 0.9%. (a) Templeton World fund has over 250 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly
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