10. A population of raw scores is normally distributed with μ =0 60 and = 14. Determine the z scores for the following raw scores taken from that population:
12. For the following z scores, determine the percentage of scores that lie between the mean and the z score:
14. Given that a population of scores is normally distributed with μ =110 and =8, determine the following:
a. The percentile rank of a score of 120
b. The percentage of scores that are below a score of 99
c. The percentage of scores that are between a score of 101 and 122
d. The percentage of scores that are between a score of 114 and 124
e. The score in the population above which 5% of the scores lie
22. Anthony is deciding whether to go to graduate school in business or law. He has taken nationally administered aptitude tests for both fields. Anthony’s scores along with the national norms are shown here. Based solely on Anthony’s relative standing on these tests, which field should he enter? Assume that the scores on both tests are normally distributed.
Field µ σ Anthony’s Scores
Business 68 4.2 80.4
Law 85 3.6 89.8
9. Which of the following are examples of independent events?
a. Obtaining a 3 and a 4 in one roll of two fair dice
b. Obtaining an ace and a king in that order by drawing twice without replacement from a deck of cards
c. Obtaining an ace and a king in that order by drawing twice with replacement from a deck of cards
d. A cloudy sky followed by rain
e. A full moon and eating a hamburger
10. Which of the following are examples of mutually exclusive events?
a. Obtaining a 4 and a 7 in one draw from a deck of ordinary playing cards
b. Obtaining a 3 and a 4 in one roll of two fair dice
c. Being male and becoming pregnant
13. If you draw a single card once from a deck of ordinary playing cards, what is the probability that it will be
a. The ace of diamonds?
b. A 10?
c. A queen or a heart?
d. A 3 or a black card?
14. If you roll two fair dice once, what is the probability that you will obtain
a. A 2 on die 1 and a 5 on die 2?
b. A 2 and a 5 without regard to which die has the 2 or 5?
18. You want to call a friend on the telephone. You remember the first three digits of her phone number, but you have forgotten the last four digits. What is the probability that you will get the correct number merely by guessing once?
p(A and B and C and D) =.1x .1x .1 x.1 .0001
25. Assume the IQ scores of the students at your university are normally distributed, with µ =115 and σ = 8. If you randomly sample one score from this distribution, what is the probability it will be
a. Higher than 130?
b. Between 110 and 125?
c. Lower than 100?
26. A standardized test measuring mathematics proficiency in sixth graders is administered nationally. The results show a normal distribution of scores, with µ =50 and σ = 5.8. If one score is randomly sampled from this population, what is the probability it will be
a. Higher than 62?
b. Between 40 and65?
c. Lower than 45?
2. What are the five conditions necessary for the binomial distribution to be appropriate?
5. Using Table B, if N = 12 and P =0.50,
a. What is the probability of getting exactly 10 P events?
b. What is the probability of getting 11 or 12 P events?
c. What is the probability of getting at least 10 P events?
d. What is the probability of getting a result as extreme as or more extreme than 10 P events?
8. An individual flips nine fair coins. If she allows only a head or a tail with each coin,
a. What is the probability they all will fall heads?
b. What is the probability there will be seven or more heads?
c. What is the probability there will be a result as extreme as or more extreme than seven heads?
12. A student is taking a true/false exam with 15 questions. If he guesses on each question, what is the probability he will get at least 13 questions correct?
16. A manufacturer of valves admits that its quality control has gone radically “downhill” such that currently the probability of producing a defective valve is 0.50. If it manufactures 1 million valves in a month and you randomly sample from these valves 10,000 samples, each composed of 15 valves,
a. In how many samples would you expect to find exactly 13 good valves?
b. In how many samples would you expect to find at least 13 good valves?