Week 3: Discrete Data Probability Distributions
Thirty-five percent of US adults have little confidence in their cars. You randomly select ten US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly six and then five the probability that it is (2) more than 7. - (1) 0.069 (2) 0.005 - (1) 0.069 (2) 0.974 - (1) 0.021 (2) 0.005 - (1) 0.021 (2) 0.026
(1) 0.069 (2) 0.005
Eighty-two percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 7 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual? - 0, 1, 2, 3 - 1, 2, 3 - 0, 1, 2, 7 - 1, 2, 3, 4
0, 1, 2, 3
Bea's Herbs and Teas offers five teas at a tea tasting. X is the number of teas a customer purchases after the tasting. Based on information from previous tastings, the pmf of X is shown below. X - 0 - 1 - 2 - 3 - 4 - 5 p(X)0.05 - 0.1 - 0.2 - 0.15 - 0.2 - 0.3 1. What is the cdf value F(0)=p(X≤0)? 0 0.05 Cannot determine from the information provided
0.05
Bea's Herbs and Teas offers five teas at a tea tasting. X is the number of teas a customer purchases after the tasting. Based on information from previous tastings, the pmf of X is shown below. X - 0 - 1 - 2 - 3 - 4 - 5 p(X)0.05 - 0.1 - 0.2 - 0.15 - 0.2 - 0.3 5. What is F(4)−F(2)? 0 0.15 0.35
0.35
Bea's Herbs and Teas offers five teas at a tea tasting. X is the number of teas a customer purchases after the tasting. Based on information from previous tastings, the pmf of X is shown below. X - 0 - 1 - 2 - 3 - 4 - 5 p(X)0.05 - 0.1 - 0.2 - 0.15 - 0.2 - 0.3 3. What is the correct value for F(3)? 0.15 0.35 0.5
0.5
Consider the following table: Defects in batch / Probability 2 / 0.35 3 / 0.23 4 / 0.20 5 / 0.09 6 / 0.07 7 / 0.06 Given this probability distribution, what is the probability that there will be less than 4 defects in batch? - 0.20 - 0.44 - 0.58 - 0.18
0.58
2. What is the probability that the displayed rating is 5 stars? 70 0.70 0.07
0.70
Bea's Herbs and Teas offers five teas at a tea tasting. X is the number of teas a customer purchases after the tasting. Based on information from previous tastings, the pmf of X is shown below. X - 0 - 1 - 2 - 3 - 4 - 5 p(X)0.05 - 0.1 - 0.2 - 0.15 - 0.2 - 0.3 What is F(6)? 0 0.3 1
1
7. In binomial probabilities, q represents _______. the negative probability p-1 the probability of x 1-p
1-p
4. If Alex can purchase up to 2 ice cream cones and the probabilities that he/she purchases 0, 1, or 2 are 0.10, 0.50, and 0.40, what is the mean number of cones that he/she will purchase? 1.0 1.5 0.7 1.3
1.3
Off the production line, there is a 4.6% chance that a candle is defective. If the company selected 50 candles off the line, what is the standard deviation of the number of defective candles in the group? - 1.48 - 1.10 - 2.30 - 2.19
1.48
Consider the following table: Defects in batch / Probability 2 / 0.35 3 / 0.23 4 / 0.20 5 / 0.09 6 / 0.07 7 / 0.06 - 2.27 - 4.50 - 1.51 - 3.48
1.51
Consider the following table: Defects in batch / Probability 0 / 0.05 1 / 0.18 2 / 0.29 3 / 0.24 4 / 0.13 5 / 0.11 Find the variance of this variable - 2.55 - 1.35 - 1.83 - 2.58
1.83
Consider the following table: Age Group - Frequency 18-29 / 9831 30-39 / 7845 40-49 / 6869 50-59 / 6323 60-60 / 5410 70 and over / 5279 If you created the probability distribution for these data, what would be the probability of 60-69? - 13.0% - 18.9% - 12.7% - 15.2%
13.0%
The probability of a potential employee passing a drug test is 91%. If you selected 15 potential employees and gave them a drug test, how many would you expect to pass the test? - 14 employees - 15 employees - 13 employees - 12 employees
14 employees
Consider the following table: Weekly hours worked - Probability 1-30 (avg. 22) / 0.08 31-40 (avg 35) / 0.16 41-50 (avg 46) / 0.72 51 and over (avg 61) / 0.04 Find the mean of this variable. - 49.2 - 42.9 - 44.2 - 41.0
42.9
A survey found that 31% of all teens buy some (pop) at least once each week. Seven teens are randomly selected. The random variable represents the number of teens who buy soda (pop) at least once each week. What is the value of n? - 7 - x, the counter - 0.07 - 0.31
7
It is known that 13% of all golfers play on the weekends. We select 25 golfers and count the number of golfers who play on weekends. For this binomial problem, which of the following is true? - the random variable is the number of golfers who do not play on weekends. - the value of p is 0.25 - a "success" would be finding a golfer who plays on weekends. - the probability of each golfer playing on weekends changes from one golfer to another.
A "success" would be finding a golfer who plays on weekends.
3. Does the table below represent an experiment, an outcome, or a probability mass function? Stars/Probability 5/0.70 4/0.20 3/0.10 2/0.00 1/0.00 an experiment an outcome a probability mass function
A probability mass function
2. D= Distance a ball is thrown Discrete Continuous
Continuous
3. W= Weight of a watermelon Discrete Continuous
Continuous
6. B= The alcohol concentration in a person's blood Discrete Continuous
Continuous
7. Y= The water temperature at different ocean depths Discrete Continuous
Continuous
Let x represent the height of corn in Oklahoma. This would be considered what type of variable: - continuous - inferential - distributed -discrete
Continuous
1. Which of the following would be a discrete variable? Count of students in a class Amount of soup in a can Number of inches reflecting someone's height Number of cans of dog food eaten
Count of students in a class
2. Consider the example above. Grace decides she will never have a week with no earnings, but instead increases the $0 weeks to $20. If the probabilities remain the same, will the variance increase, decrease, or remain the same? Increase Decrease Remain the same
Decrease
1. X= number of red cars in a parking lot Discrete Continuous
Discrete
4. Z= Fraction of games a team wins in a 16-game football season Discrete Continuous
Discrete
5. X=1 if a person passes a driver's test and X=0 if the person fails. Discrete Continuous
Discrete
Let x represent the number of cars in a parking lot. This would be considered what type of variable: - Nonsensical - Discrete - Continuous -Lagging
Discrete
Bea's Herbs and Teas offers five teas at a tea tasting. X is the number of teas a customer purchases after the tasting. Based on information from previous tastings, the pmf of X is shown below. X - 0 - 1 - 2 - 3 - 4 - 5 p(X)0.05 - 0.1 - 0.2 - 0.15 - 0.2 - 0.3 2. What is the quantity that provides the probability a customer purchases no more than 3 teas? F(2) F(3) 1−F(3)
F(3)
4. A person observes cars that drive past. Y is assigned the car's manufacturer, which may be Ford, Chevy, Toyota, or Honda. Y is a random variable. True False
False
A radar gun records a car's speed. A sign displays the text SPEEDING or NOT SPEEDING. The text displayed is a random variable. True False
False
10. When considering if a probability distribution follows the expected distribution, we are considering the distribution's __________. shape normality symmetry goodness of fit
Goodness of fit
3. If the probabilities remain the same for each of the 3 possible X values, but Grace decides that on weeks she has less time she will still test at least 1 website instead of 0, will the expected value decrease, increase, or remain the same? - Decrease - Increase - Remain the same
Increase
8. A right skewed distribution has most of the data points to the _______ of the distribution. left middle top right
Left
4. Grace's friend Mark also begins working. His schedule is less consistent and he believes his probabilities for X=0, X=100, and X=150 will be 18, 610, and 210, respectively. He also believes he will achieve X=200 (twenty sites tested) the remaining 7.5% of the weeks. How does the expected value for Mark compare to the $105 Grace expects? - Mark's is lower at $90. - Mark has the same expected value, $105. - Mark's is higher at $120.
Mark has the same expected value, $105.
5. When conducting a binomial experiment, how many times will the experiment be repeated? infinite 2 p(x) n
N
4. Does the table below represent a probability mass function? Stars/Observed proportion 5/0.75 4/0.15 3/0.10 2/0.05 1/0.05 Yes No
No
A supplier must create metal rods that are 2.1 inches width to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are too wide, too narrow, or about right? - Yes as each rod measured would have two outcomes: too long or too short - No, as there are three possible outcomes, rather than two possible outcomes - Yes, all production line quality questions are answered with binomial experiments - No, as the probability of being about right could be different for each rod selected
No, as there are three possible outcomes, rather than two possible outcomes.
3. If Sam can purchase up to 3 ice cream cones and the probabilities that he/she purchases 0, 1, 2, or 3, are 0.20, 0.45, 0.35, and 0.05 respectively, is this a valid probability distribution? No, as they do not add to 1 Yes, as they are all positive Yes, as they are all between 0 and 1 No, as no probability is between 0 and 1.
No, as they do not add to 1
1. Is the star rating, labeled S, a discrete or a continuous random variable? a discrete random variable a continuous random variable
a discrete random variable
9. A left skewed distribution can be described as __________. a symmetrical distribution having most data in the lower values having most data in the higher values having all data to the left side of the graph
having most data in the higher values
6. The mean of a binomial distribution is found using which of the following formulas? p*q q*x p*x n*p
n*p
2. A main characteristic of a discrete probability distribution is that ___________. the probabilities add to 0 the probabilities add to 1 each probability is between -1 and +1. each probability is between 1 and 2.
the probabilities add to 1
1. Grace decides she needs to earn more money and changes her probabilities. Without knowing the probabilities, which of the following could NOT be the resulting mean? - $100 - $149 - $155
$155
6. A person wins $100 per dot on the roll of a die. Z is the amount won on a die roll. Z is a random variable. True False
True
2. he new probabilities Grace assigns are 0.05 for X=0, 0.75 for X=100, and 0.2 for X=150. What is Grace's new expected earnings? - $100 - $83.333 - $105
$105
Seven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 89.4% of all their baseballs have straight stitching. If exactly five of the seven have straight stitching, should the company stop the production line? - No, the probability of exactly five have straight stitching is not unusual - Yes, the probability of exactly having straight stitching is unusual - No, the probability of five or less having straight stitching is not unusual - Yes, the probability of five or less having straight stitching is unusual
No, the probability of exactly five have straight stitching is not unusual
3. If Grace earns $20, $100, and $150 weekly, the variance is $1409. Grace receives a guaranteed amount of $10 per week regardless of how much she works. In other words, her earnings are $30, $110, and $160 with the same probabilities. What will happen to the variance? - Becomes less than $1409 - Remains the same at $1409 - Becomes higher than $1409
Remains the same at $1409
1. Which gives the measure of the center of a distribution? the variance the mean the standard deviation
The Mean
2. A survey asks a participant to indicate eye color. Possible responses are blue, brown, or green. Y is assigned 1 for blue, 2 for brown, and 3 for green. Y is a random variable. True False
True
3. A survey asks a participant to indicate age. Y is assigned the value of the response, which ranges from 1 to 120. Y is a random variable. True False
True
5. Some airports, like John Wayne Airport in California, measure noise levels when a plane flies over houses near the airport and fine airlines that exceed thresholds. Y is assigned 1 if a plane's measured sound exceeds 100 dB, and 0 otherwise. Y is a random variable. True False
True
