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HW-1881 Statistics Problems
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1.
value:
10.00 points
The chair of the board of directors says, "There is a 50% chance this company will earn a profit, a 30% chance it will break even, and a 20% chance it will lose money next quarter."
a. Use an addition rule to find the probability the company will not lose money next quarter. (Round your answer to 2 decimal places.)
=
b. Use the complement rule to find the probability it will not lose money next quarter. (Round your answer to 2 decimal places.)
=
1.
value:
10.00 points
A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit Yellowstone Park, 40% visit the Tetons, and 35% visit both.
a. What is the probability a vacationer will visit at least one of these attractions? (Round your answer to 2 decimal places.)
Probability
b. What is the probability .35 called?
c. Are the events mutually exclusive?
1.
value:
10.00 points
P(A1) = .20, P(A2) = .40, and P(A3) = .40. P(B1|A1) = .25. P(B1|A2) = .05, and P(B1|A3) = .10.
Use Bayes' theorem to determine P(A3|B1). (Round your answer to 4 decimal places.)
P(A3|B1)
1.
value:
10.00 points
Solve the following:
a.
b.
9P 3
c.
7C 2
1.
value:
10.00 points
Which of these variables are discrete and which are continuous random variables?
a. The number of new accounts established by a salesperson in a year.
b. The time between customer arrivals to a bank ATM.
c. The number of customers in Big Nick’s barber shop.
d. The amount of fuel in your car’s gas tank.
e. The number of minorities on a jury.
f. The outside temperature today.
1.
value:
10.00 points
The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations.
a. What is the probability that all six arrive within 2 days? (Round your answer to 4 decimal places.)
Probability
b. What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal places.)
Probability
c. Find the mean number of letters that will arrive within 2 days. (Round your answer to 1 decimal place.)
Number of letters
d-1. Compute the variance of the number that will arrive within 2 days. (Round your answer to 3 decimal places.)
Variance
d-2. Compute the standard deviation of the number that will arrive within 2 days. (Round your answer to 4 decimal places.)
Standard Deviation
1.
value:
10.00 points
In a binomial distribution, n = 12 and π = .60.
a. Find the probability for x = 5? (Round your answer to 3 decimal places.)
Probability
b. Find the probability for x ≤ 5? (Round your answer to 3 decimal places.)
Probability
c. Find the probability for x ≥ 6? (Round your answer to 3 decimal places.)
Probability
1.
value:
10.00 points
A population consists of 15 items, 10 of which are acceptable.
In a sample of four items, what is the probability that exactly three are acceptable? Assume the samples are drawn without replacement. (Round your answer to 4 decimal places.)
Probability
1.
value:
10.00 points
According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts.
a. What is the mean amount spent on insurance?
Mean $
b. What is the standard deviation of the amount spent? (Round your answer to 2 decimal places.)
Standard deviation $
c. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.)
Probability
d. What is the probability a family spends more than $3,000 per year? (Round your answer to 4 decimal places.)
Probability
1.
value:
10.00 points
The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to 2 decimal places.)
a. About what percent of the observations lie between 55 and 65?
Percentage of observations %
b. About what percent of the observations lie between 50 and 70?
Percentage of observations %
c. About what percent of the observations lie between 45 and 75?
Percentage of observations %
1.
value:
10.00 points
A normal population has a mean of 12.2 and a standard deviation of 2.5.
a. Compute the z value associated with 14.3. (Round your answer to 2 decimal places.)
Z
b. What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal places.)
Proportion
c. What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)
Proportion
1.
value:
10.00 points
A normal population has a mean of 80.0 and a standard deviation of 14.0.
a. Compute the probability of a value between 75.0 and 90.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)
Probability
b. Compute the probability of a value of 75.0 or less. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)
Probability
c. Compute the probability of a value between 55.0 and 70.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)
Probability
1.
value:
10.00 points
For the most recent year available, the mean annual cost to attend a private university in the United States was $26,889. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500.
Ninety-five percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number.)
Amount $
Answer will be sent by email as attachment.
value:
10.00 points
The chair of the board of directors says, "There is a 50% chance this company will earn a profit, a 30% chance it will break even, and a 20% chance it will lose money next quarter."
a. Use an addition rule to find the probability the company will not lose money next quarter. (Round your answer to 2 decimal places.)
=
b. Use the complement rule to find the probability it will not lose money next quarter. (Round your answer to 2 decimal places.)
=
1.
value:
10.00 points
A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit Yellowstone Park, 40% visit the Tetons, and 35% visit both.
a. What is the probability a vacationer will visit at least one of these attractions? (Round your answer to 2 decimal places.)
Probability
b. What is the probability .35 called?
c. Are the events mutually exclusive?
1.
value:
10.00 points
P(A1) = .20, P(A2) = .40, and P(A3) = .40. P(B1|A1) = .25. P(B1|A2) = .05, and P(B1|A3) = .10.
Use Bayes' theorem to determine P(A3|B1). (Round your answer to 4 decimal places.)
P(A3|B1)
1.
value:
10.00 points
Solve the following:
a.
b.
9P 3
c.
7C 2
1.
value:
10.00 points
Which of these variables are discrete and which are continuous random variables?
a. The number of new accounts established by a salesperson in a year.
b. The time between customer arrivals to a bank ATM.
c. The number of customers in Big Nick’s barber shop.
d. The amount of fuel in your car’s gas tank.
e. The number of minorities on a jury.
f. The outside temperature today.
1.
value:
10.00 points
The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations.
a. What is the probability that all six arrive within 2 days? (Round your answer to 4 decimal places.)
Probability
b. What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal places.)
Probability
c. Find the mean number of letters that will arrive within 2 days. (Round your answer to 1 decimal place.)
Number of letters
d-1. Compute the variance of the number that will arrive within 2 days. (Round your answer to 3 decimal places.)
Variance
d-2. Compute the standard deviation of the number that will arrive within 2 days. (Round your answer to 4 decimal places.)
Standard Deviation
1.
value:
10.00 points
In a binomial distribution, n = 12 and π = .60.
a. Find the probability for x = 5? (Round your answer to 3 decimal places.)
Probability
b. Find the probability for x ≤ 5? (Round your answer to 3 decimal places.)
Probability
c. Find the probability for x ≥ 6? (Round your answer to 3 decimal places.)
Probability
1.
value:
10.00 points
A population consists of 15 items, 10 of which are acceptable.
In a sample of four items, what is the probability that exactly three are acceptable? Assume the samples are drawn without replacement. (Round your answer to 4 decimal places.)
Probability
1.
value:
10.00 points
According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts.
a. What is the mean amount spent on insurance?
Mean $
b. What is the standard deviation of the amount spent? (Round your answer to 2 decimal places.)
Standard deviation $
c. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.)
Probability
d. What is the probability a family spends more than $3,000 per year? (Round your answer to 4 decimal places.)
Probability
1.
value:
10.00 points
The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to 2 decimal places.)
a. About what percent of the observations lie between 55 and 65?
Percentage of observations %
b. About what percent of the observations lie between 50 and 70?
Percentage of observations %
c. About what percent of the observations lie between 45 and 75?
Percentage of observations %
1.
value:
10.00 points
A normal population has a mean of 12.2 and a standard deviation of 2.5.
a. Compute the z value associated with 14.3. (Round your answer to 2 decimal places.)
Z
b. What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal places.)
Proportion
c. What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)
Proportion
1.
value:
10.00 points
A normal population has a mean of 80.0 and a standard deviation of 14.0.
a. Compute the probability of a value between 75.0 and 90.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)
Probability
b. Compute the probability of a value of 75.0 or less. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)
Probability
c. Compute the probability of a value between 55.0 and 70.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)
Probability
1.
value:
10.00 points
For the most recent year available, the mean annual cost to attend a private university in the United States was $26,889. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500.
Ninety-five percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number.)
Amount $
Answer will be sent by email as attachment.
