a P X3 2 A salesman has found that the probability of a sale

(a) P (X>3)

2. A salesman has found that the probability of a sale on a single contract is 0.07. If the salesman contacts 100 people,

(a) What is the probability that she will make atleast one sale?

(b) What is the expected number of sales?

(c) What is the variance of number of sales?

3. Suppose your travel time from home to school follows a normal distribution with mean of 15 minutesand standard deviation of 2.3 minutes.

(a) If you leave for school 12 minutes before your class start. What is the probability that you willbe late for class (hint: look up the normal table)

(b) How long long before class start should you leave home so that you arelate only 10% of the time ( hint: fint the probability from the normal table to get the corresponding z-score, then transform it back to travel time)

P.S. PLEASE LEAV GREAT EXPLANATIONS AND CLEAR STEP BY STEP PROCESS OF HOW YOU DID EACH QUESTION!!!

Solution

A)

For this exponential pdf, we have

F(x) = 1 - exp[-(x - 3)]

Thus,

P(x>3) = 1 - F(3) = 1 - [1 - exp [-(3-3)]]

P(x>3) = 1 [ANSWER]

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b)

P(x<=5) = F(5)

= 1 - exp[-(5-3)]

= 1 - exp(-2)

= 0.864664717 [ANSWER]

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