A. Scores of high school students on a national mathematics exam in Egypt were normally distributed with a mean of 86 and a standard deviation of 4.

1. What is the probability that a randomly selected student will have a score of 80 or higher?
2. If there were 97,680 students with scores higher than 91, how many students took the test?

B. In a study of television viewing habits among married couples, a researcher found that for a popular Saturday night program, 25% of the husbands viewed the program regularly and 30% of the wives viewed the program regularly. The study found that, for couples where the husband watches the program regularly, 80% of the wives also watch regularly. What is the probability that both the husband and the wife watch the program regularly?

Solution Summary

What is the probability that both the husband and the wife watch the program regularly?

Binomial Probabilities
These procedures show how to get binomial probabilities associated with n = 5 trials when the probability of a success on any given trial is π = 0.20.
Procedure I: Individual or cumulative probabilities for x = 2 successes.
Procedure II: Complete set of individual

I have been struggling with theses two following problems:
illustration: age a(0.00%) b(0.01-0.9%) c(>_0.10%)
d 0-19 142 7 6 155
e 20-39 47 8 41 96
f 40-59 29 8 77

Which of the following probabilities for the sample points A,B,and C could be true if A, B and C are the only sample points in an experiment?
a- P(A)= 1/8, P (B) = 1/7, P(C)= 1/10
b. P(A)= 1/4 P(B)=1/4, P(C)=1/4
c. P(A)= -1/4, P(B)= 1/2 P(C)=3/4
d. P(A)=0, P(B)= 1/14, P(C)=13/14.

A continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score.
a. x = $1000
b. x = $750
c. x = $1100
d. x = $950
e. x = $1225
2.Using the standard normal table, find the following probabilities

The Dept. of Labor has reported that 30% of the 2.1 million mathematical and computer scientists in the United States are women. If 3 individuals are randomly selected from this occupational group, and x = the number of females, determine P(x = 0), P(x = 1), P(x - 2), and P(x = 3).

Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
(A)
x 1 2 3 4
______________________________
P(x) 1/12 5/12 1/3 1/12
(B)
x 3 6 8
__________________________
P(x) 2/10 0.5 1/5

Determine whether each of the following is a proper probability distribution. If it is not, why?
a. X 0 5 10 15 20
P(X) 1/4 1/2 1/3 -1/4 1/4
b. X 0 2 4 6
P(X) 1 1.5 0.3 0.2
c. X 1 2 3
P(X) 1/4 1/2 1/4
d. X -2 3 7

Use the following contingency table:
Event A Event B
Event C 9 6
Event D 4 21
Event E 7 3
Determine the following probabilities:
a) P (A and C)
b) P (A and D)
c) P B and E)
d) P (A and B)

A new product has the following profit projections, associated probabilities, and indifference probability:
Profit Probability Indifference Probability
$150,000 .10 --
$100,000 .25 .95
$50,000 .20 .70
0 .15