Problem #1

Some studies suggested that six in 10 people are satisfied with their local bank. If 9 people are randomly selected, what is the probability that the number of satisfied with their local bank is:

a)Exactly two?

b)At most two?

c)At least three?

d)Between four and six, inclusive?

Problem #2

The annual wages of American farm laborers in 1926 were normally distributed with a mean of $586 and a standard deviation of $97. In 1926,

a)What percentage of American farm laborers had an annual wage between $500 and $700?

b)What percentage of American farm laborers had an annual wage above $400?

c)Find the 90^th percentile for the annual wages

Problem #3

In a certain animal species, the probability that a healthy adult female will have no offspring in a given year is .21, while the probabilities of 1,2,3, or 4 offspring are respectively, .18, .29, .17, and .15.

If the random variable X represents the number of offspring, find its mean, variance, and standard deviation.

Problem#5

The lengths of pregnancies for women are normally distributed with a mean of 268 days and a standard deviation of 15 days.

a)If one pregnant woman is randomly selected, find the probability that her length of pregnancy is less than 260 days

b)For a random sample of 25 women find the probability that their lengths of pregnancy have a mean that is less than 260 days

c)From a random sample of 5 women find the probability that exactly 2 of them have a length of pregnancy shorter than 260 days

Problem #6

The math SAT scores for women are normally distributed with a mean of 496 and a standard deviation of 108.

a)From a random selection of a woman who took the math portion of the SAT, find the probability that her score is above 500

b)From a random selection of 5 scores from the population of women taking the test, find the probability that all 5 scores are above 500

c)If 5 women are randomly selected, find the probability that their mean score is above 500

d)Find P₉₀, the score separating the top 10% from the bottom 90%

Probem#7

A pair of fair dice is simultaneously tossed. Find:

a)The probability that the sum of the outcomes is an even number

b)The probability that the sum of the outcomes is at least 8

c)The probability that the sum of the outcomes is an odd number or a number less than 6

d)Write the probability distribution of the random variable X representing the sum of the outcomes

Problem #8

Among 300 employees in a company 100 had Engineering degree, 110 had MBA degree, and 70 had both Engineering and MBA degrees. If an employee from this company is selected at random, find the probability that the employee

a. Has Engineering degree but not MBA..

b. Engineering or MBA degree.