QThe following are the number of fish caught by a crew on 25

Q)The following are the number of fish caught by a crew on 25 different days.

26 36 28 42 61 22 33 60 42 38 47 53 29 36 25 39 52 36 34 44 41 62 38 50 57

a) Construct a stem-and-leaf display. The numbers should be ordered in each class.

b) Draw a dot plot.

c) Find the median, quartiles, and 20th percentile.

d) Construct a boxplot

Q) 60 college students were surveyed to determine to their computer preferences. Of those surveyed, 36 have owned an Apple, 32 have owned a Dell, and 12 have owned both. Suppose a survey is chosen at random.

a)what is the probability that the student has never owned an Apple or a Dell?

b)What is the probability that the student has owned an Apple but not a Dell?

Q) Suppose that two events A & B are independent. If  P(A)= 0.6 and P(B)=0.4Find:

(a) P(A U B)

(b) P(Ac U B)

(c) P(A l Bc)

Q) A farm equipment manufacturer has 15 tractors in its warehouse. 4 of them have engine problems. If 5 of the tractors are chosen at random, what is the probability that:

a)Exactly 2 of the chosen tractors have engine problems?

b)At least 3 of the chosen tractors have engine problems?

Q) There are 6 freshman, 8 sophomores, and 11 juniors in a class. How many ways can the professor select 2 freshman, 3 sophomores, and 4 juniors to present a project?

Q) Anna, Bill, and Carlos all travel to work together 5 days a week. Anna drives 1 day, Bill drives 2, and Carlos drives 2. When Anna drives, they are late 10% of the time. When Bill drives they are late 15% of the time. When Carlos drives, they are late 8% of the time.

a)On a randomly chosen day, what is the probability that they come in late?

b)Suppose they came in late today, what is the probability that Bill drove?

Solution

4)

propotion of tractors have engine problem

= 4/15

this is a binomial distribution problem

a)

P(X=2) = 5C2 * (4/15)^2 * (11/15)^3 = 0.28044

b)

P(X>=3) = P(X=3) + P(X=4) + P(X=5)

= 5C3 * (4/15)^3 * (11/15)^2 + 5C4 * (4/15)^4 * (11/15) + 5C4 * (4/15)^5

=0.12187

5)

total number of ways

= 6C2 * 8C3 * 11C4

= 277200