Question

Question 1

Fifteen golfers are randomly selected. The random variable represents the number of golfers who only play on the weekends. For this to be a binomial experiment, what assumption needs to be made?
   The probability of golfing on the weekend is the same for all golfers
   The probability of golfing during the week is the same for all golfers
   All fifteen golfers play during the week
   The probability of being selected is the same for all fifteen golfers
  
Question 2

A survey found that 39% of all gamers play video games on their smartphones. Ten frequent gamers are randomly selected. The random variable represents the number of frequent games who play video games on their smartphones. What is the value of n?
   0.39
   x, the counter
   0.10
   10

Question 3

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 find 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
  
Question 4

Say a business wants to know if each salesperson is equally likely to make a sale. The company chooses 5 salespeople and gathers information on their sales experiences. What assumption must be made for this study’s probability results to be used in future binomial experiments?
   That for every 5 salespeople, the probability of making a sale is the same
   That the probability of each salesperson being one of the selected 5 is the same
   That 5% is the correct probability to use in future studies
   That the selected 5 have similar characteristics and sales areas as the other salespeople

Question 5

A soup company puts 12 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled?
   n=36, p=0.97, x=36
   n=36, p=0.97, x=1
   n=12, p=0.36, x=97
   n=12, p=0.97, x=0
  
Question 6

A supplier must create metal rods that are 2.3 inches width to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are the correct width or an incorrect width?
   No, as the probability of being about right could be different for each rod selected
   Yes, all production line quality questions are answered with binomial experiments
   No, as there are three possible outcomes, rather than two possible outcomes
   Yes, as each rod measured would have two outcomes: correct or incorrect
  
Question 7

In a box of 12 pens, there is one that does not work. Employees take pens as needed. The pens are returned once employees are done with them. You are the 5th employee to take a pen. Is this a binomial experiment?
   No, binomial does not include systematic selection such as “fifth”
   No, the probability of getting the broken pen changes as there is no replacement
   Yes, you are finding the probability of exactly 5 not being broken
   Yes, with replacement, the probability of getting the one that does not work is the same
  
Question 8

In a box of 12 pens, there is one that does not work. Employees take pens as needed. The pens are returned once employees are done with them. You are the 5th employee to take a pen. Is this a binomial experiment?
   No, binomial does not include systematic selection such as “fifth”
   No, the probability of getting the broken pen changes as there is no replacement
   Yes, you are finding the probability of exactly 5 not being broken
   Yes, with replacement, the probability of getting the one that does not work is the same
  
Question 9

Sixty-one percent of employees make judgments about their co-workers based on the cleanliness of their desk. You randomly select 8 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, 7, 8
   0, 1, 2, 8
   1, 2, 8
   1, 2, 7, 8
  
Question 10

Sixty-eight percent of products come off the line within product specifications. Your quality control department selects 15 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?
   Fewer than 8
   Fewer than 9
   Fewer than 11
   Fewer than 10

Question 11

The probability of a potential employee passing a drug test is 86%. If you selected 12 potential employees and gave them a drug test, how many would you expect to pass the test?
   8 employees
   9 employees
   10 employees
   11 employees
  
Question 12

Off the production line, there is a 3.7% chance that a candle is defective. If the company selected 45 candles off the line, what is the probability that fewer than 3 would be defective?
   0.975
   0.916
   0.768
   0.037

Answer 1

Question 1

The 4 Characteristics of a Binomial Experiment

• There must be a fixed number of trials. This number of trials is denoted by n.
• Each trial can have only two outcomes. These outcomes are called success and failure.
• The outcomes of each trial must be independent of each other.
• The probability of a success must remain the same for each trial.

Here we see that  The random variable represents the number of golfers who only play on the weekends, so success is if he plays on the weekends

Hence assumption needs to be made is  "The probability of golfing on the weekend is the same for all golfers"

Question 2. Here it is given that Ten frequent gamers are randomly selected. Hence sample size is n=10

Question 3. As all the assumptions of binomial are satisfied we will use binomial formula to find the required probability, here p=0.35 and n=10

Hence answer is   (1) 0.069 (2) 0.005

Question 4.

The 4 Characteristics of a Binomial Experiment

• There must be a fixed number of trials. This number of trials is denoted by n.
• Each trial can have only two outcomes. These outcomes are called success and failure.
• The outcomes of each trial must be independent of each other.
• The probability of a success must remain the same for each trial.

So answer is  That for every 5 salespeople, the probability of making a sale is the same as here we want to know if each salesperson is equally likely to make a sale