A basket contains 3 white balls, 3 yellow balls, and 4 red balls. Consider selecting one ball at a time from the basket
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5. A basket contains 3 white balls, 3
yellow balls, and 4 red balls. Consider selecting one ball at a time from the
basket. (Show all work. Just the answer, without supporting work, will receive
no credit.)
(a) Assuming the ball selection is
with replacement. What is the probability that the first ball is red and the
second ball is also red?
(b) Assuming the ball selection is
without replacement. What is the probability that the first ball is red and the
second ball is also red?
6.
There
are 1000 juniors in a college. Among the 1000 juniors, 300 students are taking
STAT200,
and 200 students are taking PSYC300. There are 100 students taking both
courses. Let S be the event that a
randomly selected student takes STAT200, and P be the event that a randomly
selected student takes PSYC300. (Show all work. Just the
answer,
without supporting work, will receive no credit.)
(a)
Provide
a written description of the complement event of (S OR P).
(b)
What
is the probability of complement event of (S OR P)?
7.
Consider
rolling a fair 6-faced die twice. Let A be the event that the product of the
two rolls is at most 5, and B be the event that the first one is an even
number.
(a)
What
is the probability that the product of the two rolls is at most 5 given that
the first one is an even number? Show all work. Just the answer, without
supporting work, will receive no credit.
(b)
Are
event A and event B independent? Explain.
8.
Answer
the following two questions. (Show all work. Just the answer, without
supporting work, will receive no credit).
(a)
Mimi
has seven books from the Statistics is Fun series. She plans on bringing three
of the seven books with her in a road trip. How many different ways can the
three books be selected?
(b)
UMUC
Stat Club must appoint a president, a vice president, and a treasurer. There
are 12 qualified candidates. How many different ways can the officers be
appointed?
9. Assume random variable x
follows a probability distribution shown in the table below. Determine the mean
and standard deviation of x. (Round the answer to two decimal places) Show all
work. Just the answer, without supporting work, will receive no credit.
x
-1
0
1
2
3
P(x)
0.1
0.1
0.3
0.2
0.3
10. Rabbits like to eat the cucumbers
in Mimi's garden. There are 12 cucumbers in her garden which will be ready to
harvest in about 10 days. Based on her experience, the probability of a
cucumber being eaten by the rabbits before harvest is 0.30.
(a) Let X be the number of cucumbers
that Mimi harvests (that is, the number of cucumbers not eaten by rabbits). As
we know, the distribution of X is a binomial probability distribution. What is
the number of trials (n), probability of successes (p) and probability of
failures (q), respectively?
(b) Find the probability that Mimi
harvests at least 8 of the 12 cucumbers. (round the answer to 3 decimal places)
Show all work. Just the answer, without supporting work, will receive no
credit.
11. The heights of pecan trees are normally
distributed with a mean of 10 feet and a standard deviation of 2 feet. Show all
work. Just the answer, without supporting work, will receive no credit.
(a) What is the probability that a
randomly selected pecan tree is between 7 and 12 feet tall? (round the answer
to 4 decimal places)
(b) Find the 60th percentile of the
pecan tree height distribution. (round the answer to 2 decimal places)
12. Based on the performanc5. A basket contains 3 white balls, 3
yellow balls, and 4 red balls. Consider selecting one ball at a time from the
basket. (Show all work. Just the answer, without supporting work, will receive
no credit.)
(a) Assuming the ball selection is
with replacement. What is the probability that the first ball is red and the
second ball is also red?
(b) Assuming the ball selection is
without replacement. What is the probability that the first ball is red and the
second ball is also red?
6.
There
are 1000 juniors in a college. Among the 1000 juniors, 300 students are taking
STAT200,
and 200 students are taking PSYC300. There are 100 students taking both
courses. Let S be the event that a
randomly selected student takes STAT200, and P be the event that a randomly
selected student takes PSYC300. (Show all work. Just the answer, without
supporting work, will receive no credit.)
(a)
Provide
a written description of the complement event of (S OR P).
(b)
What
is the probability of complement event of (S OR P)?
7.
Consider
rolling a fair 6-faced die twice. Let A be the event that the product of the
two rolls is at most 5, and B be the event that the first one is an even
number.
(a)
What
is the probability that the product of the two rolls is at most 5 given that
the first one is an even number? Show all work. Just the answer, without
supporting work, will receive no credit.
(b)
Are
event A and event B independent? Explain.
8.
Answer
the following two questions. (Show all work. Just the answer, without
supporting work, will receive no credit).
(a)
Mimi
has seven books from the Statistics is Fun series. She plans on bringing three
of the seven books with her in a road trip. How many different ways can the
three books be selected?
(b)
UMUC
Stat Club must appoint a president, a vice president, and a treasurer. There
are 12 qualified candidates. How many different ways can the officers be
appointed?
9. Assume random variable x
follows a probability distribution shown in the table below. Determine the mean
and standard deviation of x. (Round the answer to two decimal places) Show all work.
Just the answer, without supporting work, will receive no credit.
x
-1
0
1
2
3
P(x)
0.1
0.1
0.3
0.2
0.3
10. Rabbits like to eat the cucumbers
in Mimi's garden. There are 12 cucumbers in her garden which will be ready to
harvest in about 10 days. Based on her experience, the probability of a
cucumber being eaten by the rabbits before harvest is 0.30.
(a) Let X be the number of cucumbers
that Mimi harvests (that is, the number of cucumbers not eaten by rabbits). As
we know, the distribution of X is a binomial probability distribution. What is
the number of trials (n), probability of successes (p) and probability of
failures (q), respectively?
(b) Find the probability that Mimi
harvests at least 8 of the 12 cucumbers. (round the answer to 3 decimal places)
Show all work. Just the answer, without supporting work, will receive no
credit.
11. The heights of pecan trees are normally
distributed with a mean of 10 feet and a standard deviation of 2 feet. Show all
work. Just the answer, without supporting work, will receive no credit.
(a) What is the probability that a
randomly selected pecan tree is between 7 and 12 feet tall? (round the answer
to 4 decimal places)
(b) Find the 60th percentile of the
pecan tree height
distribution.
(round the answer to 2 decimal places)
12. Based on the performance of all
individuals who tested between July 1, 2013 and June 30, 2016, the GRE
Quantitative Reasoning scores are normally distributed with a mean of 152.57
and a standard deviation of 9.02. Show all work. Just the answer, without
supporting work, will receive no credit.
(a) Consider all random samples of 49 test
scores. What is the standard deviation of the sample means? (Round your answer
to three decimal places)
(b) What is the probability that 49
randomly selected test scores will have a mean test score that is
greater
than 153? (Round your answer to four decimal places)
13. In a study designed to test the
effectiveness of acupuncture for treating migraine, 225 patients were randomly
selected and treated with acupuncture. After one-month treatment, the number of
migraine attacks for the group had a mean of 2 and standard deviation of 1.5.
Construct a 95% confidence interval estimate of the mean number of migraine
attacks for people treated with acupuncture. Show all work. Just the answer, without
supporting work, will receive no credit.
14. Mimi conducted a survey on a
random sample of 100 adults. 60 adults in the sample chose banana as his / her
favorite fruit. Construct a 90% confidence interval estimate of the proportion
of adults whose favorite fruit is banana. Show all work. Just the answer,
without supporting work, will receive no credit.
15. A researcher claims the
proportion of auto accidents that involve teenage drivers is less than 20%. ABC
Insurance Company checks police records on 300 randomly selected auto accidents
and notes that teenagers were at the wheel in 50 of them.
Assume
the company wants to use a 0.05 significance level to test the researcher's
claim.
(a) Identify the null hypothesis and
the alternative hypothesis.
(b) Determine the test statistic.
Show all work; writing the correct test statistic, without supporting work,
will receive no credit.
(c) Determine the P-value for this
test. Show all work; writing the correct P-value, without supporting work, will
receive no credit.
(d) Is there sufficient evidence to
support the claim that the proportion of auto accidents that involve teenage
drivers is less than 20%? Explain.e of all individuals who tested between July
1, 2013 and June 30, 2016, the GRE Quantitative Reasoning scores are normally
distributed with a mean of 152.57 and a standard deviation of 9.02. Show all
work. Just the answer, without supporting work, will receive no credit.
(a) Consider all random samples of
49 test scores. What is
the
standard deviation of the sample means? (Round your answer to three decimal
places)
(b) What is the probability that 49
randomly selected test scores will have a mean test score that is
greater
than 153? (Round your answer to four decimal places)
13. In a study designed to test the
effectiveness of acupuncture for treating migraine, 225 patients were randomly
selected and treated with acupuncture. After one-month treatment, the number of
migraine attacks for the group had a mean of 2 and standard deviation of 1.5.
Construct a 95% confidence interval estimate of the mean number of migraine
attacks for people treated with acupuncture. Show all work. Just the answer,
without supporting work, will receive no credit.
14. Mimi conducted a survey on a
random sample of 100 adults. 60 adults in the sample chose banana as his / her
favorite fruit. Construct a 90% confidence interval estimate of the proportion
of adults whose favorite fruit is banana. Show all work. Just the answer,
without supporting work, will receive no credit.
15. A researcher claims the
proportion of auto accidents that involve teenage drivers is less than 20%. ABC
Insurance Company checks police records on 300 randomly selected auto accidents
and notes that teenagers were at the wheel in 50 of them.
Assume
the company wants to use a 0.05 significance level to test the researcher's
claim.
(a) Identify the null hypothesis and
the alternative hypothesis.
(b) Determine the test statistic.
Show all work; writing the correct test statistic, without supporting work,
will receive no credit.
(c) Determine the P-value for this
test. Show all work; writing the correct P-value, without supporting work, will
receive no credit.
(d) Is there sufficient evidence to
support the claim that the proportion of auto accidents that involve teenage
drivers is less than 20%? Explain.
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