CHAPTER 4INTRODUCTION TO PROBABILITY
MULTIPLE CHOICE
1. Each individual outcome of an experiment is called
a. the sample space
b. a sample point
c. an experiment
d. an individual
ANS: B
PTS: 1
TOP: Probability Concepts
2. The collection of all possible sa
Z test Single mean
As part of your work for an environmental awareness group, you want to test a claim that the
mean waste generated by adults in the U.S. is more than 3.5 pounds per day. In a random
sample of 10 adults in the U.S., you find that mean was
Test For Single Proportion
the claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.30,
and the sample statistics include n= 1297 subjects with 402 saying that the smoked a cigarette in the
past week.
find the test
Test For Single Proportion
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the
study 446 babies were born, and 242 of them were girls.Use the sample data with a 0.01
significance level to test the claim that w
Test For Single Proportion
A physician claims that 13.6% of all pregnant females smoke during their pregnancy. A
random sample of 400 pregnant women revealed that 60 of them are smoking while
pregnant. Test the physician's claim at the 0.05 level of signi
Test for single mean
Consider the hypothesis test given by
H0: u=530
H1: u does not equal 530
In a random sample of 81 subjects, the sample mean is found to be 524.Also, the population
standard deviation is o=27
1. Determine the P-value for this test. Is
Test For Single Mean
At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden
was told, You can average more than $80 a day in tips.D Assume the standard deviation
of the population distribution is $3.24. Over the first 35 days
Test For Single Mean
Suppose you know that for the entire United States, the mean age of the population is 32,
with a standard deviation of 14.5 years. Since many retired people move to Florida, you
believe that the mean age of all Florida residents is gr
Test For Significance of Different Of Proportion
A random telephone survey asked 208 drivers if they run red lights. Of the 48 drivers who
were 35 years old or younger, 32 admitted that they run red lights. Eighty-six of the 160
drivers that were older th
Test For Significance of Different Of Proportion
A certain researcher thinks that the proportion of women who say that the earth is getting
warmer is greater than the proportion of men.
In a random sample of 250 women, 70% said that the earth is getting w
Run Test
Q)
During a 45-day production period in a cement plant, test cubes were taken each day and the
compressive
strengths of the test cubes were determined with the following results (units are kg/cm^2(data
from Hald (1952).
Test the hypothesis of ran
Normal Distribution
Assume that you are a member of the president%u2019s economic advisers. The president
has
asked your team to propose a welfare program to aid the disadvantaged, which consists of
a money payment to the nation%u2019s poorest 15%. The qu
Normal Distribution Problems
The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
1. What is the probability that a randomly person has an IQ between 85 and 115?
2. Find the 90th percentile of the IQ distribution.
3. I
Normal Distribution
An insurance company knows that in the entire population of millions of homeowners, the
mean annual loss from fire is U= $450 and the standard deviation of the loss is & S.D=
$1350. The distribution of losses is strongly right skewed:
Mean, Mode, Median
For the set of data cfw_8, 10, 11, 12, 13, 14, 15, 9, 15, 18, 51 calculate the values of the mean,
median, mode, standard deviation, IQR and range.
What are the best measures of center and spread for this data set. Explain why you
choos
Hypothesis Testing
Q)
The contingency table below presents voters reactions to a new property tax plan according to
party affiliation. Test the null hypothesis that there is no relationship between party affiliation
and voter reaction, using the one perce
Hypothesis Test
Q)
Are the two sample means sufficient to conclude that the
educational modes are significantly different? Give reasons for
your decision. t = 4 SE[M1-M2] = 2 alpha 0.05 t critical = plus or
minus 2.01 n1=10, M1=93, S12=20 (in S the 1 is w
Empirical Rule
Use the Empirical Rule, if the mean weight of 2 year puppies is 22 pounds with a variance of
6.25 pounds, what is the probability that a puppy will weight between 17 and 27 pounds?
Answer)
u=22 s=sqrt(6.25)=2.5
x1=17
z1=(x1-u)/s = -2
x2=27
Distribution Function
Q)
Suppose X has the following distribution function:
F(x) = cfw_ 0
cfw_ x(0.1 + 0.2x)
cfw_1
x<= 0
0 < x <= 2
x >2
Verify F is distribution function
Find f(x)
Find P( 0.5 <= X <= 1.5)
Find the mean and variance of X
Answer)
It is con
Stats Demand Analysis
A video rental store has two video cameras available for customers to rent. Historically, demand for
cameras has followed this distribution. The revenue per rental is $40. If a customer wants a camera
and none is available, the store
Confidence Interval
Use the given degree of confidence and sample data to construct a confidence interval for the
population mean . Assume that the population has a normal distribution
N=12 X=20.9 S=4.7, 99% confidence
Solution)
alpha,a=0.01
Za/2 = Z0.005
Confidence Interval
Carry at least four digits after the decimal in your calculations. Answers may vary slightly
due to rounding.
In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was
found that 36 out of 818 fish di
Confidence Interval For Proportion
Of 367 randomly selected medical students, 30 said that they planned to work in a rural
community. Find a 95% confidence interval for the true proportion of all medical students
who plan to work in a rural community.
Ans
Confidence Interval
Q)
For this problem, carry at least four digits after the decimal in your calculations. Answers
may vary slightly due to rounding.
In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was
found that
Confidence Interval
A pharmaceutical company wanted to estimate the population mean of monthly sales for their
250 sales people. 38 sales people were randomly selected. Their mean monthly sales was
$10,805 with a population standard deviation of $1,058. C
Confidence Interval
Generate 50 samples (rows) of five observations each from a normal distribution with m = 30
and s = 2. Thus, each row contains one sample of five observations selected randomly from a
normal distribution. Then calculate a 90% confidenc
Confidence Ineterval
A random sample of 116 lightning flashes in a certain region resulted in a sample average
radar echo duration of 0.86 sec and a sample standard deviation of 0.37 sec. Calculate a 99%
(two-sided) confidence interval for the true averag
Binomial Distribution
E-mail fraud (phishing) is becoming an increasing problem for users of the internet. Suppose
that 70% of all internet users experience e-mail fraud. If 50 internet users were randomly
selected, what is the probability that no more th