Question

In: Statistics and Probability

-A consumer organization inspecting new cars found that many had appearance defects​ (dents, scratches, paint​ chips,...

-A consumer organization inspecting new cars found that many had appearance defects​ (dents, scratches, paint​ chips, etc.). While none had more than three of these​defects,

6​% had​ three, 12% had​ two, and 26% had one defect. Find the expected number of appearance defects in a new car and the standard deviation. Compute the expected value of the number of appearance defects.

​E(appearance

​defects)equals=. 68.68

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

Compute the standard deviation of the number of appearance defects.

​SD(appearance

​defects)equals= _____________________

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

-A salesman normally makes a sale​ (closes) on 70% 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 sixth attempt.​

b) He closes his first presentation on his fifth 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 11% of the population is​ left-handed. If they select a sample of 99 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 third person chosen.The probability is _____________________

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

​b) There are some lefties among the 99 people.The probability is _______________________

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

​c) The first lefty is the second or third person. The probability is __________________________

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

​d) There are exactly 3 lefties in the group. The probability is __________________________

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

​e) There are at least 3 lefties in the group. The probability is __________________________

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

​f) There are no more than 3 lefties in the group. The probability is _________________________

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

Solutions

Expert Solution

The distribution of appearance defects​ is

The expected value is

Now the second moment is

The standard deviation is

The probability that the salesman closes on his attempt has geometric distribution. The PMF is

. Here

a) The probability that he closes for the first time on his sixth attempt is

The probability that fails to close for the first time on his sixth attempt is

b)The probability that he closes for the first time on his fifth attempt is

c) The probability that he closes for the first time on his second attempt is

d) The required probability is

We are required to solve only one question. Please post the remaining questions as another post.

I answered 2.


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