# Understanding and calculating probabilities

1. A certain company reduced its management staff from 18 managers to 12. The company claimed that the 6 managers were randomly selected for job termination. However, the 6 managers chosen are the 6 oldest managers among the 18 that were employed. What is the probability that when 6 oldest managers are randomly selected from a group of 18 different aged managers, the 6 oldest ones are selected and is this event "Unusual"?

2. A container has one each $1, $2, $5, $10, $20, $50, and $100 dollar bills. It costs $30 to reach in and draw a bill. What is the expected value of the draw?

3. Use the given data to find the equation of the regression line.

x 3 1 4 4 5

y 2 -2 5 4 8

4. The following data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting a Republican given that a female was selected?

Republicans Democrats Independents

Male 7 9 0

Female 66 19 3

5. The diameter of a steel ball is normally distributed, with a mean of 0.4 inch and a variance of 0.0004. What is the probability that the diameter of a randomly selected pipe will exceed 0.44 inch?

6. An IQ test is designed so that the mean is 100 and the standard deviation of 20 for population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence, that the sample mean is with 5 IQ points of the true mean (E=5). Assume that

7. The score on a test are normally distributed with a mean of 75 and a standard deviation of 6. If the professor wishes to give A's to the top 4%, what would be the cutoff score be for A's?

8. BSA Venture Crew 829 has 4 boys and 3 girls. In how many ways can they choose a president, vice president, and secretary, in that order; if the president must be a girl and the other officers must be boys?

9. What is the probability of obtaining exactly 3 heads in 4 flips of a coin, given that at least two are heads?

10. Assume that women's height are normally distrusted with a mean given by µ = 64.6 inches and standard deviation given by what area under the normal curve corresponds to the probability that a woman's height is between 63.7 inches and 64.7?

11. The weights of the 100 boys in our Boy Scout are normally distributed, with a mean of 170 pounds and a standard deviation of 5 pounds. How many boys would you expect to have weight between 162 pounds and 178? What is the probability that a boy picked a random weight less than 165 pounds?

12. The Jones family has 4 boys. What is the probability that the next child of the Jones family will be a boy, given that they have already 4 boys in a row?