Question

An​ e-commerce Web site claims that

4

​%

of people who visit the site make a purchase. Complete parts a through e below based on a random sample of

15

people who visited the Web site.

a. What is the probability that none of the people will make a

purchase​?

The probability is

nothing

.

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

b. What is the probability that less than 3 people will make a​ purchase?

The probability is

nothing

.

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

c. What is the probability that more than 1 person will make a​ purchase?

The probability is

nothing

.

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

d. Construct a histogram for this distribution. Choose the correct graph below.

A.

Binomial Probability Distribution

0369121500.51Number of purchasersProbability

A histogram titled Binomial Probability Distribution has a horizontal axis labeled Number of purchasers from 0 to 15 in increments of 1 and a vertical axis labeled Probability from 0 to 1 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the Number of purchasers is listed first and the height is listed second: 0, 0.54; 1, 0.88; 2, 0.98; 3, 1; 4, 1; 5, 1; 6, 1; 7, 1; 8, 1; 9, 1; 10, 1; 11, 1; 12, 1; 13, 1; 14, 1; 15, 1. All heights are approximate.

B.

Binomial Probability Distribution

0369121500.5Number of purchasersProbability

A histogram titled Binomial Probability Distribution has a horizontal axis labeled Number of purchasers from 0 to 15 in increments of 1 and a vertical axis labeled Probability from 0 to 1 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the Number of purchasers is listed first and the height is listed second: 0, 0; 1, 0; 2, 0; 3, 0; 4, 0; 5, 0; 6, 0; 7, 0; 8, 0; 9, 0; 10, 0; 11, 0; 12, 0.02; 13, 0.1; 14, 0.34; 15, 0.54. All heights are approximate.

C.

Binomial Probability Distribution

0369121500.5Number of purchasersProbability

A histogram titled Binomial Probability Distribution has a horizontal axis labeled Number of purchasers from 0 to 15 in increments of 1 and a vertical axis labeled Probability from 0 to 1 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. The heights of the vertical bars are as follows, where the Number of purchasers is listed first and the height is listed second: 0, 0.54; 1, 0.34; 2, 0.1; 3, 0.02; 4, 0; 5, 0; 6, 0; 7, 0; 8, 0; 9, 0; 10, 0; 11, 0; 12, 0; 13, 0; 14, 0; 15, 0. All heights are approximate.

e. Suppose that out of the

15

​customers,

7

made a purchase. What conclusions can be drawn about the​ sample?

The probability that

7

out of

15

customers make a purchase is

nothing

​,

assuming that

4

​%

of customers make a purchase.​ Therefore, it is

▼

not likely

likely

that randomly selecting

15

customers would result in

7

customers who made a purchase.

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

Click to select your answer(s).

Answer 1

here this is binomial with parameter n=15 and p=0.04

a)

P(X=0)=

(nCx)px(1−p)(n-x)    =

0.5421

b)

P(X<3)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.9797

c)

P(X>=2)=1-P(X<=1)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.1191

d)

e)

The probability that 7 out of 15 customers make a purchase is is 0.0000

Therefore, it is not likely that randomly selecting 15 customers would result in 7 customers who made a purchase.