uestion:Hi, Could you please answer the following questions with ALL WORKING? I really focused on the working out of the answers.

Practice Questions 1

1.If the random variableXis normally distributed with a mean of 75 and a standard deviation of 8, thenP(X 78) is:

2.Only 60% of patients receive such a call a nurse. Of the patients called, 90% pay on time, while only 30% of those not called pay on time. The Dr.has just received a payment on time from a patient.

What is the probability that the nurse didnotcall this patient?

3.On 40% of his calls, there is no answer or the line is busy. He sells the auto insurance policy to 5% of the remaining calls. For what proportion of calls does he make a sale?

4.A portfolio is composed of two shares. The following parameters associated with the returns of the two shares are given.

Share

Proportion of portfolio

Share 1: 45%

Share 2: 55%

Mean

Share 1: 0.10

Share 2: 0.20

Standard deviation

Share1: 0.02

Share 2: 0.15

The mean return of the portfolio is:

5.Suppose P(A) = 0.10, P(B) = 0.75, and P(B|A) = 0.80. Find P(AB) is:

6.Four PhD graduates are applying for a lectureship position in a college. The four applicants are A, B, C and D. Employing the subjective approach, Jerry has assigned the following probabilities that these applicants will be hired:

P(A) = 0.41

P(B) = 0.10

P(C) = 0.27

P(D) = 0.22

The probability that either B or C are hired is:

7.Given thatZis a standard normal random variable,P(Z>1.75) is:

8.LetXbe a random variable with the following probability distribution:

X

5

10

15

P(X)

0.45

0.30

0.25

The variance of 4X-3 is:

9.A multiple-choice quiz has 20 questions. Each question has four possible answers, of which only one is correct. The expected number of correct answers by sheer guesswork is:

10.The amount of time it takes for a respondent to complete survey is uniformly distributed between 50 and 70 minutes. One respondent is selected at random. The probability that the respondent requires more than 65 minutes to complete the quiz is: