Exam 15: Random Variables

Janet is planning to rent a booth at a festival for a day to sell clothes that she has made.She sells jackets for $215 and skirts for $115.Her past experiences suggests that the total number of jackets sold will have a mean of 6.3 with a standard deviation of 1.6,and the total number of skirts sold will have a mean of 11.7 with a standard deviation of 3.0.The cost of renting the booth for the day is $180.What are the mean and standard deviation of her net income? [Hint: you should first define random variables and use them to express her net income]

A company bids on two contracts.It anticipates a profit of $70,000 if it gets the larger contract and a profit of $40,000 if it gets the smaller contract.It estimates that there's a 30% chance of winning the larger contract and a 50% chance of winning the smaller contract.Find the company's expected profit.Assume that the contracts will be awarded independently.

A carnival game offers a $80 cash prize for anyone who can break a balloon by throwing a dart at it.It costs $5 to play and you're willing to spend up to $20 trying to win.You estimate that you have a 12% chance of hitting the balloon on any throw.Create a probability model for the amount you will win.Assume that throws are independent of each other.Round to four decimal places if necessary.

The amount of money that Maria earns in a week is a random variable,X,with a mean of $900 and a standard deviation of .The amount of money that Daniel earns in a week is a random variable,Y,with a mean of $800 and a standard deviation of .The difference,X - Y,between Maria's weekly income and Daniel's weekly income is a random variable with a mean of $900 - $800 = $100.If the incomes are independent of one another,which of the following shows the correct method for calculating the standard deviation of the random variable X - Y?

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 2X.

Sue Anne owns a medium-sized business.The probability model below describes the number of employees that may call in sick on any given day. What is the expected value of the number of employees calling in sick each day?

The number of golf balls ordered by customers of a pro shop has the following probability distribution.

You pick a card from a deck.If you get a face card,you win $15.If you get an ace,you win $30 plus an extra $60 for the ace of hearts.For any other card you win nothing.Find the expected amount you will win.

A company sells light bulbs in packages of 20 and estimates that the mean number of defective light bulbs in a package is 0.6 with a standard deviation of 0.7.If a customer buys 12 packages,what are the expected value and standard deviation of the number of defective light bulbs? Assume that packages are independent of each other.

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable X + 2Y .Round to two decimal places if necessary.

Sue Anne owns a medium-sized business.The probability model below describes the number of employees that may call in sick on any given day. What is the standard deviation of the number of employees calling in sick each day?

A company bids on two contracts.It anticipates a profit of $50,000 if it gets the larger contract and a profit of $10,000 if it gets the smaller contract.It estimates that there's a 10% chance of winning the larger contract and a 70% chance of winning the smaller contract.Create a probability model for the company's profit.Assume that the contracts will be awarded independently.

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 4X + 19.Round to two decimal places if necessary.

Miguel buys a large bottle and a small bottle of juice.The amount of juice that the manufacturer puts in the large bottle is a random variable with a mean of 1,018 ml and a standard deviation of 9 ml.The amount of juice that the manufacturer puts in the small bottle is a random variable with a mean of 506 ml and a standard deviation of 3 ml.Let the random variable T represent the total amount of juice in the two bottles.Suppose that you use a Normal model to determine the probability that the total amount of juice,T,in the two bottles is more than 1,543.0 ml.Which of the following assumptions are needed to find the probability in this way? A: The amount of juice in the large bottle is independent of the amount of juice in the small bottle. B: The amount of juice in each bottle follows a Normal model. C: The amount of juice in the large bottle is greater than the amount of juice in the small bottle.

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 3X - Y .Round to two decimal places if necessary.

Jo is a hairstylist.The probability model below describes the number of clients that she may see in a day. What is the expected value of the number of clients that Jo sees per day?

Your school's soccer team plays two games against another soccer team .The probability that your team wins the first game is 0.6.If your team wins the first game,the probability that they also win the second game is 0.7.If your team loses the first game,the probability that they win the second game is 0.5.Let the random variable X be the number of games won by your team.Find the probability model for X.

An insurance policy costs $140 per year,and will pay policyholders $15,000 if they suffer a major injury (resulting in hospitalization)or $7,000 if they suffer a minor injury (resulting in lost time from work).The company estimates that each year 1 in every 2,200 policyholders will have a major injury and 1 in every 400 a minor injury.What is the company's expected profit on this policy?