Chapter 6 Probability

Probability 68

Three fair coins are tossed. If all land "heads," the player wins $10, and if exactly two land heads, the player wins $5. If it costs $4 to play, what is the expected outcome after four games.

• Loss of $0.875

• Loss of $1.00

• Loss of $3.50

• Win of $2.25

• Win of $9.00

Probability 69

Suppose a manufacturer knows that 20 percent of the circuit boards coming off the assembly line have a minor defect. If an inspector keeps inspecting boards until he comes upon one with the defect, what is the probability he will have to inspect at most three boards?

• .128

• .384

• .488

• .512

• .896

Probability 75

Which of the following are true statements?

1.) The sampling distribution of the difference x̄₁-x̄₂ has a mean equal to the difference of the population means.

2.) The sampling distribution of the difference x̄₁-x̄₂ has a standard deviation equal to the sum of the population standard deviations.

3.) The sampling distribution of the difference x̄₁-x̄₂ has a standard deviation equal to the difference of the population standard deviations.

• 1 only

• 2 only

• 3 only

• 1 and 2

• 1 and 3

Probability 74

Suppose X and Y are independent random variables, both with normal distributions. if X has mean 30 with standard deviation 6, and Y has mean 25 with standard deviation 4, what is the probability that a randomly generated value of X is greater than a randomly generated value of Y?

• .5000

• .6914

• .7440

• .7560

• .8413

Probability 77

Five managers and five employees are on a grievance committee. A three-person subcommittee is formed by a random selection from the ten committee members. What is the probability that all three members of the subcommittee are managers?

• 1/12

• 1/16

• 3/16

• 5/16

• 1/2

Probability 43

Suppose we have a random variable X where the probability associated with the value k is 12C_k (.34)^k(.66)^12-k for k=0,..., 12. What is the mean of X?

*check packet for the binomial coefficient 12C_k

• 0.34

• 0.66

• 4.08

• 7.92

• None of the above

Probability 45

Given a random variable X taking three possible values x₁, x₂, x₃, which of the following statements must be true?

1.) x₁ + x₂ + x₃ = 1

2.) Σ(X)=1/3Σx_i

3.) var(X)=1/3Σ(x_i-x̄)²

• 1 only

• 3 only

• 2 and 3

• 1, 2, and 3

• None of the statements are true.

Probability 48

There are 8,253 men and 10,327 women at a state university. If 43 percent of the men and 27 percent of the women are business majors, what is the expected number of business majors in a random sample of 200 students?

• 31.7

• 34.1

• 63.4

• 68.2

• 70.0

Probability 63

For which of the following is a binomial an appropriate model?

• The number of heads in ten tosses of an unfair coin weighted so that heads comes up twice as often as tails.

• The number of hits in five at-bats where the probability of a hit is either .352 or .324 depending upon whether the pitcher is right-handed or left-handed.

• The number of tosses of a fair coin before heads appears on two consecutive tosses.

• The number of snowy days in a given week.

• The binomial is appropriate in all of the above.

• $2,380

• $3,500

• $5,355

• $8,109

• $37,485