Question

A salesman normally makes a sale​ (closes) on 75​% of his presentations. Assuming the presentations are​ independent, find the probability of each of the following.

​a) He fails to close for the first time on his fifth attempt.

​b) He closes his first presentation on his fourth attempt.

​c) The first presentation he closes will be on his second attempt.

​d) The first presentation he closes will be on one of his first three attempts.

A manufacturer of game controllers is concerned that its controller may be difficult for​ left-handed users. They set out to find lefties to test. About 13​% of the population is​ left-handed. If they select a sample of 6 customers at random in their​ stores, what is the probability of each of the outcomes described in parts a through f​ below?

a) The first lefty is the fourth person chosen.

The probability is _____________

​(Round to four decimal places as​ needed.)

The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. Complete parts a and b below.

Repair Calls 1 2 3 4

Probability .1 .4 .3 .2

​b) What is the standard​ deviation?

The standard deviation is ____________

​(Round to two decimal places as​ needed.)

Answer 1

The probability that the salesman closes on any given presentation is p=0.75

The probability that the salesman does not close on any given presentation is 1-p=1-0.75=0.25

a) The probability that he fails to close for the first time on his fifth attempt is same as the probability that he closes on his first 4 attempts and fails on his 5th attempt.

ans: The probability that he fails to close for the first time on his fifth attempt is 0.0791

b) The probability that he closes his first presentation on his fourth attempt is same as he fails on his first 3 attempts and closes on the 4th

ans: The probability that he closes his first presentation on his fourth attempt is 0.0117

c) The probability that the first presentation he closes will be on his second attempt is

ans: The probability that the first presentation he closes will be on his second attempt is 0.1875

d) The probability that the first presentation he closes will be on one of his first three attempts is same as the probability that he closes at least 1 presentation on his first 3 attempts.

ans: he probability that the first presentation he closes will be on one of his first three attempts is 0.9844

The probability that a randomly selected customer is left handed is 0.13

The probability that a randomly selected customer is right handed is 1-0.13=0.87

The probability that the first lefty is the fourth person chosen is same as the probability that first 3 chosen are right handed and the 4th customer is a lefty

ans: The probability that the first lefty is the fourth person chosen is 0.0856

Let X= the number of repair calls that an appliance repair shop may receive during an hour

The distribution of X is

Repair Calls (x)	Probability P(x)
1	0.1
2	0.4
3	0.3
4	0.2

The expected value of X is

The expected value of is

The variance of X is

The standard deviation of X is

ans: the standard deviation is 0.92