The amount of money that Maria earns in a week is a random variable with a mean of $980 and a standard deviation of $25.The amount of money that Elena earns in a week is a random variable with a mean of $800 and a standard deviation of $10.
You would like to use a Normal model to determine the probability that Maria's weekly income is at least $233.85 more than Elena's weekly income (the probability that the difference M - E is at least $233.85).
Which of the following assumptions are needed?
A: Maria's weekly earnings are independent of Elena's weekly earnings.
B: Maria's weekly earnings and Elena's weekly earnings follow a Normal model.
C: Maria's weekly earnings are greater than Elena's weekly earnings.
A)A and C
B)A only
C)B only
D)A,B,and C
E)A and B

Question

Quizplus · Accepted Answer

We need to assume that both Maria's and Elena's weekly earnings follow a Normal model and that they are independent random variables. Therefore, we need to assume both A and B. We do not need to assume that Maria's weekly earnings are greater than Elena's weekly earnings (choice C) since we are interested in the probability of the difference between their earnings.

The Amount of Money That Maria Earns in a Week