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Math 227 Sp’08 Instr:Wong, D. Final Exam Name:_______________________

#1 True/False

1pt.

each ______________ (a) The standard deviation, s, is not effected by extreme data.

______________ (b) If the data distribution is skewed to one-side, the median

should be used for the center of measurements.

______________ (c) 5/3 cannot be an answer for a probability.

______________ (d) On a five possible answers multiple-choice question, the

probability of answering the question correctly by random

guessing is 1/2.

______________ (e) With the same level of confidence and the same standard

deviation, as n increases the width of the confidence interval

increases.

______________ (f) The claim is always the same as Ho.

______________ (g) If the population distribution is not normally distributed,

the distribution for the sampling mean will be approximately

normally distributed for n = 20.

______________ (h) t – distribution depends on the sample size.

#2 A card is selected randomly from a deck of cards, what is the probability that a face

5pt. card (Jack, Queen, King) or a club will be selected.

#3 Two dice are tossed. What is the probability of getting a sum of 8?

5pt.

#4 A carton contains 12 eggs, 3 of which are cracked. If we randomly select 2 eggs,

5pt. one after the other without replacement, what is the probability that both of the

cracked eggs are selected?

#5 Listed below are the Titanic mortality data.

Men Women Boys Girls

Survived 332 318 29 27

Died 1360 104 35 18

5pt. (a) If we randomly select someone who was aboard the Titanic, what is the

probability of getting a man or a person who survived?

4pt. (b) What is the probability of getting a woman, given the selected person died?

#6 Find P(x = 3) for the following probability distribution table.

4pt.

x 1 2 3 4

P(x) 0.12 0.21 ? 0.18

#7 It was found that 55% of American victims of health care fraud are senior

citizens. If 20 victims are randomly selected,

5pt. (a) find the probability that exactly 14 are senior citizens.

2pt. (b) find ( and ( for this binomial distribution.

#8 The average amount of rain per year in Greenville is 49 inches. The standard

7pt. deviation is 8 inches. Find the probability that next year Greenville will receive

the amount of rainfall in between 46 and 54 inches.

#9 If the average score of a reading test is 122.6 with the standard deviation of 18, find

6pt. the cutoff-score for the bottom 5%. Assume the variable is normally distributed.

#10 The average annual salary in Pennsylvania was $24,393 in 1992. Assume that

6pt. salaries were normally distributed for a certain group of wage earners, and the

standard deviation of this group was $4362. Find the probability that, for a

randomly selected sample of 25 individuals, the mean salary was less than

$26,000.

#11 A researcher is interested in estimating the average monthly salary of sports reporters

5pt. in a large city. He wants to be 99% confident that his estimate is correct. If ( = $1100,

how large a sample must be selected if he wishes to be accurate to within $150?

#12 A sample of 500 nursing applications included 60 from men. Find the 90% confidence

5pt. interval of the true proportion of men who applied to the nursing program.

#13 An attorney claims that more than 25% of all lawyers advertise. A sample of 200

12pt. lawyers in a certain city showed that 63 had used some form of advertising.

At ( = 0.05, is there enough evidence to support the attorney’s claim?

#14 A state executive claims that the average number of acres in western Pennsylvania

state parks is less than 2000 acres. A random sample of five parks is selected, and

the number of acres is shown.

959 1187 493 6249 541

4pt. (a) Use your calculator to find the sample mean and the sample standard deviation.

12pt. (b) At ( = 0.01, is there enough evidence to support the claim?

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