14. (b) What is the probability that 20 cars chosen at random will have a meanload weight x of less than 74.5 tons of coal?(c) Interpretation Suppose the weight of coal in one car was less than74.5 tons. Would that fact make you suspect that the loader had slippedout 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 yoususpect 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 UnitedStates, 112th edition).(a) What is the probability that an 18-year-old man selected at random isbetween 67 and 69 inches tall?(b) If a random sample of nine 18-year-old men is selected, what is theprobability 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 leveof glucose in the blood (milligrams per deciliter of blood) after a 12-hour fasAssume that for people under 50 years old, x has a distribution that is approximately normal, with mean u =(based on information from Diagnostic Tests with Nursing Applications,edited by S. Loeb, Springhouse). A test result x < 40 is an indication ofsevere 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 weekapart. What can we say about the probability distribution of x? Hint: SeeTheorem 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). Didthe probabilities decrease as n increased? Explain what this might implyif you were a doctor or a nurse. If a patient had a test result of x < 40based on five tests, explain why either you are looking at an extremelyrare event or (more likely) the person has a case of excess insulin.85 and estimated standard deviation o =253 tests taken a week apart.5 tests taken a week apart.16.| Medical: White Blood Cells Let x be a random variable that representswhite blood cell count per cubic milliliter of whole blood. Assume that xhas a distribution that is approximately normal, with mean u7500 andestimated standard deviation o =1750 (see reference in Problem 15). A testresult 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 x for two tests taken about a weekapart. What can we say about the probability distribution of x? What isthe probability of x < 3500?(c) Repeat part (b) for n(d) Interpretation Compare your answers to parts (a), (b), and (c). How diethe probabilities change as n increased? If a person had I < 3500 basedon 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 inkilograms (kg) of healthy adult female deer (does) in December in MesaVerde National Park. Then x has a distribution that is approximately normal,with mean u63.0 kg and standard deviation o7.1 kg (Source: TheMule Deer of Mesa Verde National Park, by G. W. Mierau and J. L. Schmidt

14. Given data: Let X denotes the heights of 18-year old men. X is normally distributed with mean…

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?

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?

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Equations and inequalities describe the relationship between two mathematical expressions.

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Question

14.

(b) What is the probability that 20 cars chosen at random will have a mean
load weight x of less than 74.5 tons of coal?
(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 leve
of glucose in the blood (milligrams per deciliter of blood) after a 12-hour fas
Assume that for people under 50 years old, x has a distribution that is approx
imately normal, with mean u =
(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 x 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 die
the probabilities change as n increased? If a person had I < 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

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