Probability Distribution
Binomial Distribution
Z-score of a data point
sample proportions
probability proportions
100
State the two reasons why this is a valid probability distribution.
SLide 1
100
Which of the following are the correct properties that make this a binomial. Check the properties that make this a binomial (you should only check 4 boxes): (8 points)
Slide 4 # 1
100
ACT (American College Testing) scores are known to be normally distributed with a mean of 21 and a standard deviation of 5.
1. What is the probability that a randomly selected person will score between 19 and 30 on the ACT? (Give your final answer rounded to 3-4 decimal places). (4 points)
SLide 6 #1
100
The proportion of Americans that are women is assumed to be known to be 51%. A marketing survey telephones 100 people at random.
1. Find the mean of the sampling distribution of the sample proportion. (Round to 2 decimal places.) (2 points)
Slide 9 #1
100
The University of South Carolina posts information about the incoming freshman class each year on the school’s website. The information for the class of 2025 freshmen states that this is the 2nd largest enrollment of freshman on the Columbia campus. It also states that the population mean high school grade point average was 4.4. Assume a random sample of 49 was taken and assume a population standard deviation of 0.63 was known (note the standard deviation was made up). (Site: UofSC’s freshman class brings record GPAs - UofSC News & Events | University of South Carolina)
1. Which of the following allows us to know that the sampling distribution of the sample means is normally distributed? (2.5 points)
a. n > 30 b. n < 30 c. nσ ≥ 15 and n(1-σ) ≥ 15 d. σ > 0.50
slide 11 #1
200
slide one #2
200
The University of South Carolina posts information about the incoming freshman class each year on the school’s website. The information for the class of 2025 freshmen states that this is the 2nd largest enrollment of freshman on the Columbia campus. It also states that 16% (0.16) of these freshman are first generation college students. Assume we study only 8 freshman at a time and the students are independent of each other. (Site: UofSC’s freshman class brings record GPAs - UofSC News & Events | University of South Carolina)
What is the probability that none of the freshmen studied are first generation college students? (Round your answer to 3-4 decimal places).
slide 4 #1
200
ACT (American College Testing) scores are known to be normally distributed with a mean of 21 and a standard deviation of 5.
2. At what ACT score will 90.32% of scores fall below? (Give your final answer rounded to 2 decimal places). (4 points)
Slide 6 #2
200
The proportion of Americans that are women is assumed to be known to be 51%. A marketing survey telephones 100 people at random.
2. Find the standard error of the sampling distribution of the sample proportion.(Round to 2 decimal places).(2 points)
slide 9 #2
200
The University of South Carolina posts information about the incoming freshman class each year on the school’s website. The information for the class of 2025 freshmen states that this is the 2nd largest enrollment of freshman on the Columbia campus. It also states that the population mean high school grade point average was 4.4. Assume a random sample of 49 was taken and assume a population standard deviation of 0.63 was known (note the standard deviation was made up). (Site: UofSC’s freshman class brings record GPAs - UofSC News & Events | University of South Carolina)
2. What is the mean of the sampling distribution of the sample means? (Round your answer to 2 decimal places if needed) (3 points)
slide 11 #2
300
What does the expected value in question ? (2.5 points)
a. The expected number of tires every customers that enters the shop is going to get in the short run.
b. The expected average number of tires customers that enter the shop will get in the short run.
c. The expected number of tires every customers that enters the shop is going to get in the long run.
d. The expected average number of tires customers that enter the shop will get in the long run.
Slide 1 #3
300
The University of South Carolina posts information about the incoming freshman class each year on the school’s website. The information for the class of 2025 freshmen states that this is the 2nd largest enrollment of freshman on the Columbia campus. It also states that 16% (0.16) of these freshman are first generation college students. Assume we study only 8 freshman at a time and the students are independent of each other. (Site: UofSC’s freshman class brings record GPAs - UofSC News & Events | University of South Carolina)
What is the mean number of freshmen (out of 8) that are first generation college students? (Round your answer to 2 decimal places). (3 points)
slid 4 #3
300
Toolworkers are subject to work-related injuries. One disorder, causes by strains to the hands and wrists, is called carpal tunnel syndrome. Assume the mean cost of this disorder to employers and insurers is known to be $30,000 with a standard deviation of $9,000. Suppose these costs known to be normally distributed.
2. What is the probability that the cost will be less than $15,000? Round to 3 or 4 decimal places.
slide 7 #2
300
The proportion of Americans that are women is assumed to be known to be 51%. A marketing survey telephones 100 people at random.
3. Would it be unusual to get a sample that had a proportion of women of 63%? Justify your answer referencing a z-score. (3 points)
slde 9 #3
300
The University of South Carolina posts information about the incoming freshman class each year on the school’s website. The information for the class of 2025 freshmen states that this is the 2nd largest enrollment of freshman on the Columbia campus. It also states that the population mean high school grade point average was 4.4. Assume a random sample of 49 was taken and assume a population standard deviation of 0.63 was known (note the standard deviation was made up). (Site: UofSC’s freshman class brings record GPAs - UofSC News & Events | University of South Carolina)
3. What is the probability that a random sample of 49 had a sample mean greater than 4.25? (Round your final answer to 3-4 decimal places) (4 points)
Slide 11 #3
400
What is the probability that freshman at the college are registered for at least 5 classes their first semester? (Round to 1 decimal place). (2 points)
slide 2 #3
400
Assume 60% of all pizza stores offer online ordering. Suppose 10 independent pizza stores are randomly selected and we want to calculate the likelihood that a particular number of stores (out of the 10) that offer online ordering.
This question follows a binomial distribution because there are . (2 points)
a. two possible outcomes: success = does not offer online ordering; failure = does offer online ordering.
b. two possible outcomes: success = does offer online ordering; failure = does not offer online ordering.
c. one possible outcome: success = does offer online ordering.
d. one possible outcome: success = does not offer online ordering.
slide 5 #4
400
Toolworkers are subject to work-related injuries. One disorder, causes by strains to the hands and wrists, is called carpal tunnel syndrome. Assume the mean cost of this disorder to employers and insurers is known to be $30,000 with a standard deviation of $9,000. Suppose these costs known to be normally distributed.
3. What is the probability that the cost will be more than $40,000? Round to 3 or 4 decimal places.
Slide 7#3
400
The proportion of Americans that are women is assumed to be known to be 51%. A marketing survey telephones 100 people at random.
4. What is the probability that a sample proportion would be less than 49%? (Round to 3 or 4 decimal places). (4 points).
Slide 9 #4
400
A particular bus route has a mean time for the trip of 40 minutes with a standard deviation of 16 minutes. Assume a sample of size 64 was taken.
2. Find the standard error of the sampling distribution of the sample means for samples of size 64. (Round your final answer to 2 decimal places) (3 points)
slide 12 #2
500
Calculate the expected number of classes full time freshman at the college are registered for their first semester
slide 2 #4
500
Assume 60% of all pizza stores offer online ordering. Suppose 10 independent pizza stores are randomly selected and we want to calculate the likelihood that a particular number of stores (out of the 10) that offer online ordering.
What is the mean number of pizza stores, out of 10, that offer online ordering? (Round your final answer to 2 decimal places). Note: you do not have to interpret the value just calculate it. (3 points)
slide 5 #7
500
Toolworkers are subject to work-related injuries. One disorder, causes by strains to the hands and wrists, is called carpal tunnel syndrome. Assume the mean cost of this disorder to employers and insurers is known to be $30,000 with a standard deviation of $9,000. Suppose these costs known to be normally distributed.
4. What is the probability that the cost will be between $15,000 and $40,000? Round to 3 or 4 decimal place.
slide 7 #4
500
The University of South Carolina posts information about the incoming freshman class each year on the school’s website. The information for the most recent incoming class of freshmen states that this is the 2nd largest enrollment of freshman on the Columbia campus. It also states that 53% (0.53) of these freshmen are from South Carolina. Assume we want to pull a random sample of 100 freshmen. (Site: UofSC’s freshman class brings record GPAs - UofSC News & Events | University of South Carolina)
3. Would a sample proportion of 40% (0.40) be considered an unusual value? Justify your answer referencing a z-score. (4 points)
slide 10 #3
500
A particular bus route has a mean time for the trip of 40 minutes with a standard deviation of 16 minutes. Assume a sample of size 64 was taken.
3. In a sample of 64, if you wanted to find the probability that a sample mean time for the trip was between 38 and 45 minutes what is the correct z-score formula to use? (2 points)
slide 11#3