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 assumption A to ensure that the two earnings are independent, and assumption B to use a Normal model for their distribution. Assumption C is not needed, as we are only interested in the difference between the earnings, not their individual values.

The Amount of Money That Maria Earns in a Week M−EM - EM−E

The Amount of Money That Maria Earns in a Week $M - E$