Combining Two Random Variables Answers

There are frogs and koi in a pond, and the number of frogs and the number of koi in the pond are independent. Let X represent the number of frogs in any given week, and let Y represent the number of koi in any given week. X has a mean of 28 with a standard deviation of 2.7, and Y has a mean of 15 with a standard deviation of 1.6. Which answer choice correctly calculates and interprets the standard deviation of the difference, D = X - Y?

Two machines, X and Y, produce earbuds. Let X represent the diameter of an earbud produced by machine X, and let Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of 0.6 mm, and Y has a mean of 15.2 mm with a standard deviation of 0.2 mm. Which answer choice correctly calculates and interprets the mean of the difference, D = X – Y?

Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S – T.What is the probability that Soledad sends more texts on a randomly selected day?

Elroy enjoys roller skating and weight training. Let X represent the number of hours he spends roller skating weekly, and let Y represent the number of hours he spends weight training weekly. The mean of X is 5 hours, and the mean of Y is 7 hours. Which answer choice correctly calculates and interprets the mean of the sum, S = X + Y?

JT has two jobs. He mows yards and washes cars in his neighborhood. Let X represent the amount of weekly earnings for mowing yards, and let Y represent the amount of weekly earnings for washing cars. The mean of X is $60, and the mean of Y is $35. Which answer choice correctly calculates and interprets the mean of the sum, S = X + Y?

A hotel has two different ice machines that fill buckets of ice independently of each other. Let A represent the amount of ice in a bucket filled by machine A, and let B represent the amount of ice in a bucket filled by machine B. Which of the following choices explains the meaning of independent random variables in context?

Lynnetta gets paid weekly for completing household chores. The amount of money she earns for doing dishes, D, is approximately Normally distributed with a mean of $53 and a standard deviation of $3.60. The amount of money she earns for doing laundry, L, is approximately Normally distributed with a mean of $47 and a standard deviation of $4.10. Assume that D and L are independent random variables.What is the probability that Lynnetta will earn more than $110 in a randomly selected week?

Tonya and Emily each have an online jewelry store. Let T represent the amount of money Tonya earns daily, and let E represent the amount of money Emily earns daily. The mean difference, D = T – E, of the amount of money that Tonya and Emily earn on a typical day is $312. What is the correct interpretation of this value?

The weight of panda bears, P, is approximately Normally distributed with a mean of 185 pounds and a standard deviation of 12.3 pounds. The weight of koala bears, K, is approximately Normally distributed with a mean of 21.5 pounds and a standard deviation of 4.8 pounds. Suppose a zookeeper randomly chooses a panda and a koala bear, where P and K are independent random variables.What is the probability that the total weight for the two animals is 225 pounds or more?

Sisters Sharon and Karen enjoy sleeping. Let X represent the number of hours Sharon sleeps each night, and let Y represent the number of hours Karen sleeps each night. The mean of X is 7.9, and the mean of Y is 8.4. Which answer choice correctly calculates and interprets the mean of the sum, S = X + Y?