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Math 227 Summer 2014 Practice Final

#1 True/False

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

______________ (b) The correlation coefficient is between -1 and 1

______________ (c) 6/5 cannot be an answer for a probability.

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

probability of answering the question correctly by random

guessing is 1/2.

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

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

card (Jack, Queen, King) or a heart will be selected.

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

#4 The height of a pediatrician 3-yr-old females are approximately normally distributed with

mean 38.72 inches and standard deviation 3.17 inches. Find the height of a 3 yr old at the

20th percentile.

#5 Listed below are the Titanic mortality data.

Men Women Boys Girls

Survived 332 318 29 27

Died 1360 104 35 18

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

probability of getting a man or a person who survived?

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

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

x 1 2 3 4

P(x) 0.12 0.21 ? 0.18

(b) Find the mean of the probability distribution.

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

citizens. If 20 victims are randomly selected,

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

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

#8 Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-through. Certainly, the faster the cars get through the drive-through, the more the opportunity for making money. QSR Magazine studied drive-through times for fast food restaurants and found Wendy’s had the best time, with a mean time spent in the drive-though of 138.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 29 seconds,

a) What is the probability that a randomly selected car will spend between 2 and 3 minutes?

b) Less than 100 seconds?

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

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

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

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

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

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

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

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

#15 Heights of men have a bell-shaped distribution with a mean of 176 cm and a standard deviation of 7

cm. Using the empirical rule, what is the approximate percentage of men between 155 cm and 197

cm?

#16 If Z is a standard normal variable, find the probability that Z is greater than -2.89.

#17 Determine whether the given procedure results in a binomial distribution. Why or why not?

Toss a coin 25 times, keeping track of the number of tails.

#18 There are 9 members on the board of directors for a hospital. If they must elect a chairperson, vice chairperson, and a secretary, how many different slates of candidates are possible?

#19 For the following data: 14 15 8 11 8 8 9 1 12 8 7 15

(a) Find the Mea

(b) Find the Median

(c) Find the Mode

(d) Find the Five-number summary (Low, Q1, Q2, Q3, High)

(e) Construct a boxplot

#20 Find the z value to the left of the mean so that 60.64% of the area under the distribution

curve lies to the right of it.

#21 Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are

normally distributed with a standard deviation of $1500, find the probability that the student

makes between $13,000 and $14000.

#22 Given the equation of the regression line [pic] and the correlation

coefficient [pic], find the best predicted value of y for x = 2.00. What is r?

#23 State the four requirements for a Binomial Experiment.

#24 Find the p-value for a right tailed test with observed [pic]

#25 One survey showed that among 785 randomly selected subjects who completed four

years of college, 144 smoke. Use [pic] to test the claim that the percentage (p) of

smoking among those with four years of college is less than the 27% rate for the general

population.

#26 The mean is [pic] and the standard deviation is [pic], find the probability that X is between 135.0 an d143.2. X has a normal distribution

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