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WorksheetsStatistics End of Week 15 Assessment
Total questions: 20
Worksheet time: 29mins
Fatima conducts emissions inspections on cars. She finds that 6% of the cars fail the inspection. Let C be the number of cars Fatima inspects until a car fails an inspection. Assume that the results of each inspection are independent.
Find the probability that the first failed inspection occurs on Fatima's 5th inspection.
You may round your answer to the nearest hundredth.
(a)
As a part of a customer loyalty program, a restaurant's computer chooses orders at random to receive a free appetizer. Each order has a 1 in 18 chance of receiving a free appetizer. (Each order is limited to one free appetizer.) Let X be the number of orders the restaurant fills in a day until they give away the first appetizer. Assume that each order getting the appetizer is independent.
Find the probability that the restaurant first gives away an appetizer on the 6th order of the day.
You may round your answer to the nearest hundredth.
(a)
Minenhle registers vehicles for the Department of Transportation. Leased vehicles make up 6% of the vehicles she registers. Let V be the number of vehicles Minenhle registers in a day until she first registers a leased vehicle. Assume the status of each vehicle is independent.
Find the probability that Minenhle registers a leased vehicle within the first 3 vehicles of the day.
You may round your answer to the nearest hundredth.
(a)
Jeremiah makes 25% of the three-point shots he attempts. For a warm-up, Jeremiah likes to shoot three-point shots until he makes one. Let M be the number of shots it takes Jeremiah to make his first three-point shot. Assume that the results of each shot are independent.
Find the probability that it takes Jeremiah more than 6 attempts to make his first shot.
You may round your answer to the nearest hundredth.
(a)
Ravi sells real estate. Based on previous data, he knows that 5% of home tours result in a sale. Assume that the results of these tours are independent from each other.
Which of the following choices are binomial random variables?
Choose all answers that apply:
Take a random sample of 3 tours and let K = the number of tours that result in a sale.
Take a random sample of 30 tours and let L = the number of tours that result in a sale.
Take a random sample of 3 tours and let M = the amount of money (in dollars) generated by the tours.
None of the mentioned examples
Katarina tosses a thumbtack on the ground 20 times to see if it lands on its side or if it lands with the point facing up (there are no other possible outcomes). Let S = the number of times it lands on its side.
Is S a binomial variable? Why or why not?
Choose 1 answer:
Each trial isn't being classified as a success or failure, so S is not a binomial variable.
There is no fixed number of trials, so S is not a binomial variable.
The trials are not independent, so S is not a binomial variable.
This situation satisfies each of the conditions for a binomial variable, so S has a binomial distribution.
Leo selects 25 grandparents at random from his town to interview. In the town, 35% of the grandparents have their grandchildren living with them. Let G be the number of grandparents Leo interviews whose grandchildren are living with them.
What type of variable is G?
Binomial
Geometric
Neither
Alma wrote a phone app. She has noticed that 3% of the users who download her app upgrade it the same day. Let N be the number of customers who download Alma's app until one upgrades it on the same day. Assume that the probability of each user's upgrades are independent.
What type of variable is N?
Binomial
Geometric
Neither
Kiera is contacting the poll workers from the last election to see whether they are willing to work in the next election. During the last election, 42%of the poll workers were under 60 years old. Let W be the number of poll workers Kiera contacts before reaching one that is 60years old or older. Assume that each poll worker's age is independent.
Find the mean and standard deviation of W.
Round your answers to one decimal place.
Mean = 2.4
Standard deviation = 1.8
Mean = 2.4
Standard deviation = 3.3
Mean = 1.7
Standard deviation = 1.1
Mean = 1.7
Standard deviation = 1.2
A basketball player is practicing 3-pointers. If the probability that he successfully scores each shot is 54 , what is the expected value of the points he scores after throwing 100 shots?
48
60
150
240
80
Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu.
Find the probability that at least four of the 25 patients actually have the flu.
(give your answer to 4 decimal places)
(a)
In a binomial experiment, the probability of a success in each trial is 0.3, and 20 trials are performed. What is the expected number of successful trials?
(a)
