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

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

jeongho jeong · Accepted Answer

Final Answer : E, Explanation :  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.

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