Question

7. Which of the following is a characteristic of a binomial probability experiment?
A. Each trial has at least two possible outcomes
B. P(success) = 1 – P(failure)
C. The binomial random variable x is the count of the number of trials that occur
D. The result of one trial affects the probability of success on any other trial
Answer:
8. If the random variable z is the standard normal score, which of the following probabilities could easily be determined without referring to a table?
A. P(z > 5)
B. P(z < 1.43)
C. P(z < - 2.95)
D. P(z > -0.35)
Answer:
9. If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(B | A) is:
A. 1.4 B. 1.8 C. 0.714 D.0.556
Answer:

10. In which of the following binomial distributions is the normal approximation appropriate?
A. n = 100, p = 0.04
B. n = 50, p = 0.09
C. n = 75, p = 0.06
D. n = 12, p = 0.45
Answer:
Part II. Short Answers & Computational Questions
1. Classify the following as discrete or continuous random variables (4 pts)
a. The number of Nursing majors at South University
b. The time it takes to complete this assignment
c. The blood pressures of all patients admitted to a hospital on a certain day
d. The number of people who play the state lottery each day
Answer:




2. A small bag of Skittles candies has the following assortment: red (12), blue (5), orange (15), brown (0), green (16), and yellow (7). Construct the probability distribution for x. (6 pts)
Answer:
x red blue orange brown green yellow
P(x) 0.218 0.091 0.273 0 0.291 0.127

3. Find the mean and standard deviation of the following probability distribution: (4 pts)
x 1 2 3
P(x) 0.4 0.25 0.35

Answer:
4. Find the following probabilities: (4 pts)
a. Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.3 and P(A or B) = 0.75, find P(B).
b. Events A and B are defined on a common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or B) = 0.72, find P(A and B)
Answer:
5. Find the value of z such that 45% of the distribution lies between it and the mean (4pts)
Answer:




6. In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 15 patients using the drug is selected. Find the probability that: (4pts)
i. exactly three will have this mild side effect
ii. at least two will have this mild side effect.
Answer:


7. A large shipment of TV sets is accepted upon delivery if an inspection of twelve randomly selected TV sets yields no more than one defective TV. (6 pts)
i. Find the probability that this shipment is accepted if 5% of the total shipment is defective.
ii. Find the probability that this shipment is not accepted if 10% of this shipment is defective
Answer:
8. X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities: (6 pts)
i. P(x < 74.0)
ii. P(76.0 < x < 85.0)
iii. P(x>89.0)
Answer:

9. Assume that the average annual salary for a worker in the United States is $31,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $7,500. Find the following: (6 pts)
i. What percentage of Americans earn below $20,000?
ii. What percentage of Americans earn above $45,000?

Answer 1

: A ------------------------ Part II. Short

Answer 2

: x red blue orange brown green yellow P(x) 0.218 0.091 0.273 0 0.291 0.127 3. Find the mean and standard deviation of the following probability distribution: (4 pts) x 1 2 3 P(x) 0.4 0.25 0.35

Answer 3

: 9. Assume that the average annual salary for a worker in the United States is $31,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $7,500. Find the following: (6 pts) i. What percentage of Americans earn below $20,000? ii. What percentage of Americans earn above $45,000?

Answer 4

7. Which of the following is a characteristic of a binomial probability experiment? A. Each trial has at least two possible outcomes B. P(success) = 1 – P(failure) C. The binomial random variable x is the count of the number of trials that occur D. The result of one trial affects the probability of success on any other trial

Answer 5

: 0.35 --------------------------------------------------- 4. Find the following probabilities: (4 pts) a. Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.3 and P(A or B) = 0.75, find P(B). 0.75 = 0.3 + P(B) ; P(B) = 0.45 ---------------------------------------------- b. Events A and B are defined on a common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or B) = 0.72, find P(A and B)

Answer 6

s &Computational Questions 1. Classify the following as discrete or continuous random variables (4 pts) a. The number of Nursing majors at South University---discrete b. The time it takes to complete this assignment---cont c. The blood pressures of all patients admitted to a hospital on a certain day cont. d. The number of people who play the state lottery each day---discrete

Answer 7

: 8. X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities: (6 pts) i. P(x < 74.0) ii. P(76.0 < x < 85.0) iii. P(x>89.0)

Answer 8

: 2. A small bag of Skittles candies has the following assortment: red (12), blue (5), orange (15), brown (0), green (16), and yellow (7). Construct the probability distribution for x. (6 pts)

Answer 9

: 7. A large shipment of TV sets is accepted upon delivery if an inspection of twelve randomly selected TV sets yields no more than one defective TV. (6 pts) i. Find the probability that this shipment is accepted if 5% of the total shipment is defective. ii. Find the probability that this shipment is not accepted if 10% of this shipment is defective

Answer 10

: -1.645 or +1.645 ================================== Cheers, Stan H. 6. In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 15 patients using the drug is selected. Find the probability that: (4pts) i. exactly three will have this mild side effect ii. at least two will have this mild side effect.

Answer 11

: P(B | A) = [P(A and B]/P(A) = 0.25/0.45 = D ================================================================ 10. In which of the following binomial distributions is the normal approximation appropriate? A. n = 100, p = 0.04 B. n = 50, p = 0.09 C. n = 75, p = 0.06 D. n = 12, p = 0.45

Answer 12

: P(A and B) = 0.30+0.50 - 0.72 = 0.08 ------------------------------------------------------------- 5. Find the value of z such that 45% of the distribution lies between it and the mean (4pts)

Answer 13

: A --------------------------------------------------------------------------- 9. If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(B | A) is: A. 1.4 B. 1.8 C. 0.714 D.0.556

Answer 14

: B ----------------------------------------------------------------------------- 8. If the random variable z is the standard normal score, which of the following probabilities could easily be determined without referring to a table? A. P(z > 5) B. P(z < 1.43) C. P(z < - 2.95) D. P(z > -0.35)