Please show work

IV Random Variables

1. A survey of 200 people looking to purchase a new car was administered. The following results on preference were recorded.

Vehicle Make

People

Ford

50

Chevrolet

30

Toyota

60

Dodge

40

Kia

20

1. What is the probability of selecting someone who prefers Toyota?(6/20)

1. What is the probability of selecting someone who prefers Kia or Dodge?(6/20)

1. What is the probability of selecting someone who does not prefer Toyota?(14/20)

2. A study was made to investigate the number of times adult males over 30 visit a physician each year. The results for a sample were:

Number of visits

0

1

2

3 or more

Number of Adult Male

0.1

0.3

...

0.4

1. What is the probability of selecting someone who visits a physician twice a year?(0.2)
2. What is the probability of selecting someone who visits a physician?(0.9)
3. What is the probability of selecting someone who visits a physician at least 2 times?(0.6)

3. A study of 200 advertising firms revealed their incomes after taxes:

Income after Taxes

Number of Firms

Under $1 million

100

$1 million to $20 million

60

$20 million or more

40

1. What is the probability an advertising firms selected at random has under $1 million in income after taxes?(1/2)
2. What is the probability an advertising firms selected at random has not $1 million or more in income after taxes?(1/2)
3. What is the probability an advertising firms selected at random has $20 million or more or less than $1 million in income after taxes?(7/10)

4. Which table represents a probability distribution

a)

X

-20

0

10

20

P

1/5

1/5

2/5

1/5

b)

X

-3

-1

1

3

P

0.3

0.1

0.1

0.3

5. Croissant Bakery Inc. offers specially decorated cakes for birthdays, weddings, and other occasions. It also has regular cakes available in its display case. The following table gives the total number of cakes sold per day and the corresponding probability. Compute the mean, variance, and standard deviation of the number of cakes sold per day.

Number of cakes sold in a day

12

13

14

15

Probability

0.25

0.40

0.25

0.10

()

V Binomial Random Variable

1. Seven coins are tossed. What is the probability that three of them will be "heads"?(0.273)

2. Five dice are rolled. What is the probability that we will get two four times or more?(0.0033)

3. A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find:

1. The probability of making three or four sales.(0.4708)
2. The probability of making no sales. (0.0138)
3. The mean and standard deviation of number of sales in the two-hour period(3.6; 1.5875)

4. A recent survey of first-year college students found that 20 percent choose accounting as their major. Suppose we select a sample of 15 first-year students. What is the probability that

a) two selected accounting(0.2309)b)five selected accounting (0.103) c) at least one selected accounting(0.965)

5. In a recent study 90 percent of homes in Canada were found to have large-screen TVs. In a sample of nine homes, what is the probability that:

1. All nine have large-screen TVs?(0.387)
2. Less than five have large-screen TVs?(0.00089)
3. More than five have large-screen TVs?(0.992)
4. At least seven homes have large-screen TVs?(0.947)