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```MATH 2311
Final Exam Review
The probability that a randomly selected person is
left handed (the event L) is P(L) = 0.1 and the
probability that a randomly selected person is a
blonde (the event B) is P(B) = 0.3. The probability
that a randomly selected person is left handed and
a blonde is 0.02. Find the probability that a
randomly selected person either is left handed, a
blonde, or both.
Among 9 lightbulbs produced exactly two is known
not to function properly. If 3 lightbulbs are
selected randomly, find the probability that exactly
one does not function properly.
Given the following sampling distribution:
What is P(X < 3)?
Given the following sampling distribution:
Determine the mean of the distribution.
Given the following sampling distribution:
Determine the variance of the distribution.
Suppose you have a distribution, X, with mean =
75 and standard deviation = 8. Define a new
random variable Y = 2X - 15. Find the mean and
standard deviation of Y.
In testing a study technique, researchers found
that 15% of all students using it will have
increased scores. A random sample of 25 students
using the technique is selected. Find the
probability that exactly three will have increased
scores.
A manufacturer of paperclips randomly and
independently puts 200 paperclips in each box
produced. The company knows that 1 percent of
the clips will break. What is the probability that a
box will have one or fewer paperclips break?
Each year a high school selects a number of
students for a summer camp program. On
average, 60 percent of those selected attend the
program. Out of the 35 students selected, what is
the probability that exactly 15 attend the
program?
A batter has an RBI of 0.16. We want to observe
this batter during one game to see how many atbats he has before his first home run. What is the
probability that the batter’s first homerun is on his
third time to the plate?
The length of time needed to drive to school is
normally distributed with mean 32 minutes and
standard deviation 7 minutes. Find the probability
that it will take less than 27 minutes to drive to
school.
Find a value of c so that P(Z > c) = 0.23.
A random sample of 1000 soda cans is pulled from
an assembly line. Prior experience has shown that
the distribution of the contents has a mean of 8
ounces and a standard deviation of 0.09 ounce.
What is the probability that the mean contents of
the 1000 sample cans is less than 7.5 ounces?
In a large population, 72% of the households have
multiple cars. A simple random sample of 150
households is to be contacted and the sample
proportion computed. What is the mean and
standard deviation of the sampling distribution of
the sample proportions?
In a large population, 72% of the households have
multiple cars. A simple random sample of 150
households is to be contacted and the sample
proportion computed. What is the probability that
the sample distribution has a proportion less than
70%?
Determine the correlation coefficient of the
following data:
Determine the LSRL of the data:
Determine the residual of the data for the
value of x = 6.
Based on the tw0-way distribution table,
what percent of married people drive vans?
A simple random sample of 100 kindergarteners
indicated that 71% of them have imaginary
friends. Find the 95% confidence interval that
estimates the proportion of them that have
imaginary friends.
A test has been done to show the effectiveness of
a new drug. The treatment group, 45 people, had
25% improvement rate, and the placebo group, 35
people, had a 10% improvement rate. Determine
the 90% confidence interval for the difference in
improvement rates.
The height of 8th graders is known to have a
standard deviation of 4 inches. A simple
random sample of 81 of them is chosen and
found to have a mean height of 52 inches.
Construct a 89% confidence interval for the
mean height of 8th grade students.
A study is conducted to determine the mean
height of college students. A group of 50 men had
a mean height of 70 inches with a standard
deviation of 4 inches. A group of 40 women had a
mean height of 66 inches with a standard
deviation of 5 inches. Determine the 95%
confidence interval for the difference in mean
heights.
A company wants to determine the proportion of
people in Houston that have premium cable
service. How many people must be surveyed to
have a confidence level of 98% with a margin of
error of 3%?
A coin is flipped 200 times and landed on heads a
total of 135 times. Test the two-sided claim, with
confidence of 5%, that the coin is fair.
A gym wanted to determine if more men or
women took fitness classes. Out of 55 men
surveyed, 25 took fitness classes, and out of 75
women surveyed 45 of them took fitness classes.
Is the difference in proportions statistically
significant, with significance level of 5%?
A automated card-dealer is tested to show if it is
favoring one suit of cards. Out of 100 cards dealt,
there were 35 clubs, 15 spades, 20 hearts, and 30
diamonds. Test using a chi-squared process to
determine if the machine is dealing fairly, using
significance of 1%.
There is a claim that African-Americans are more
susceptible to heart disease. A study is conducted
where 50 African-Americans are tested, showing
that 15 have some form of heart disease, and 40
non-African-Americans were tested to show that
9 have some form of heart disease. Test this
claim, with a significance level of 5%.
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