Question: Can someone please help me with this problem? Problem 1) Suppose weekly income for students at KSU follows a Normal distribution with a mean of

Can someone please help me with this problem?

Problem 1) Suppose weekly income for students at KSU follows a Normal distribution with a mean of $225 and a standard deviation of $40.

  1. Suppose one student is randomly selected. What is the probability that this student's weekly income exceeds $310?
  2. According to the Empirical Rule, approximately 68% of students have weekly incomes between what two values?
  3. According to the Empirical Rule, approximately ____% of students have weekly incomes between $145 and $305?
  4. Suppose a student is randomly selected and his weekly income is $400. Would this be considered an outlier? Briefly support your answer.

Problem 2)Consider the discrete probability distribution shown below. The variable X represents the number of loads of laundry you do per week. Use the given distribution to answer the questions that follow.

x

0

1

2

3

4

5

P(X = x)

0.16

0.25

0.34

0.15

0.03

  1. What value for P(X = 4) makes this a valid probability distribution?
  2. What is the mean of this distribution? In other words, how many loads of laundry do you do per week, on average?
  3. Suppose a week is randomly selected. What is the probability that you do one or three loads of laundry this week?
  4. Suppose a week is randomly selected. What is the probability that you do fewer than three loads of laundry this week?

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