## There Are 15 Juniors And 20 Seniors In The Umuc Stat Club

Answer the following two questions. (Show all work. Just the answer, without supporting work, will receive no credit). (a) There are 15 juniors and 20 seniors in the UMUC Stat Club. The club is to send four representatives to the Joint Statistical Meetings. If the members of the club decide to send two juniors and two seniors, how many different groupings are possible?(b) A bike courier needs to make deliveries at 6 different locations. How many different routes can he take?

## There Are 15 Juniors And 20 Seniors In The Umuc Stat Club

1. There are 15 juniors and 20 seniors in the UMUC Stat Club. The club is to send fourrepresentatives to the Joint Statistical Meetings. a. If the members of the club decide to send two juniors and two seniors, how many different groupingsare possible?(b) A bike courier needs to make deliveries at 6 different locations. How many different routes can hetake?2. Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 cucumbers in her garden which willbe ready to harvest in about 10 days. Based on her experience, the probability of a cucumber beingeaten 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 eatenby rabbits). As we know, the distribution of X is a binomial probability distribution. What is the numberof trials (n), probability of successes (p) and probability of failures (q), respectively?(b) Find the probability that Mimi harvests at most 8 of the 10 cucumbers. (round the answer to 3decimal places)3. Assume the weights of men are normally distributed with a mean of 170 lbs and a standard deviationof 30 lbs. Show all work. Just the answer, without supporting work, will receive no credit. (a) Find the 75th percentile for the distribution of men’s weights. (b) What is the probability that a randomly selected man weighs more than 200 lbs?4. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and astandard deviation of 100. Show all work. Just the answer, without supporting work, will receive nocredit. (a) If a random sample of 64 test scores is selected, what is the standard deviation of the sample mean?(b) What is the probability that 64 randomly selected test scores will have a mean test score that isbetween 475 and 525?5. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a 90%confidence interval estimate of the proportion of adults believing in global warming6. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were treatedwith garlic tablets. Cholesterol levels were measured before and after the treatment. The changes intheir LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14. Construct a 95%confidence interval estimate of the mean change in LDL cholesterol after the garlic tablet treatment

## There are 15 juniors and 20 seniors in the UMUC Stat Club

Question
1. There are 15 juniors and 20 seniors in the UMUC Stat Club. The club is to send four
representatives to the Joint Statistical Meetings.
a. If the members of the club decide to send two juniors and two seniors, how many different groupings
are possible?
(b) A bike courier needs to make deliveries at 6 different locations. How many different routes can he
take?

2. Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 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 most 8 of the 10 cucumbers. (round the answer to 3
decimal places)

3. Assume the weights of men are normally distributed with a mean of 170 lbs and a standard deviation
of 30 lbs. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Find the 75th percentile for the distribution of men’s weights.
(b) What is the probability that a randomly selected man weighs more than 200 lbs?

4. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a
standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no
credit.
(a) If a random sample of 64 test scores is selected, what is the standard deviation of the sample mean?
(b) What is the probability that 64 randomly selected test scores will have a mean test score that is
between 475 and 525?

5. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a 90%
confidence interval estimate of the proportion of adults believing in global warming

6. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were treated
with garlic tablets. Cholesterol levels were measured before and after the treatment. The changes in
their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14. Construct a 95%
confidence interval estimate of the mean change in LDL cholesterol after the garlic tablet treatment