Download Ch 16 Probability Review with Vocabulary

Facts about the Normal Curve:
1.
Ch 5 Normal Distributions and Ch 17 Sampling Distributions
Facts about sampling distributions:
The Graduate Record Examinations (GRE) are widely used to help predict the performance of applicants to graduate schools. The
range of possible scores on a GRE is 200 to 900. The psychology department at a university finds that the scores of its applicants on
the quantitative GRE are approximately normal with mean  = 544 and standard deviation  = 103. Find the proportion of applicants
whose score X satisfies each of the following conditions:
a) X  650
b) X  440
c) 500  X  700
d) what is the 30th percentile score?
e) What score is needed to be in the top 10%?
f) Suppose we take an SRS of 50 applicants, find the probability that the mean score for the group lies between 500 and 700.
2.
The college Physical Education Department offered an Advanced First Aid course last semester. The scores on the comprehensive
final exam were normally distributed, and the z scores for some of the students are shown below:
Amara, 1.10
Ben, 1.70
Cesar, – 2.00
Dora, 0.00
Ellie, –0.80
Frank, 1.60
a)
Which of these students scored above the mean?
b) Which of these students scored on the mean?
c)
Which of these students scored below the mean?
d) Did anybody score in the top 10%? (if yes, then who?) Explain how you decided.
Answer “TRUE” if the statement is always true. If the statement is not always true, replace the BOLD with words that will make the
statement true:
_______________ a.
A large mean value () will cause a normal curve to be tall and slender.
3.
_______________ b.
For a normal distribution, 95% of all observations fall within two standard deviations of the mean.
_______________ c.
For all values greater than the mean, we will obtain a positive z-score.
4.
The physical fitness of a patient is often measured by the patient’s maximum oxygen uptake (recorded in milliliters per kilogram).
The mean maximum oxygen uptake for cardiac patients who regularly participate in sports programs was found to be 24.1 ml/kg with
a standard deviation of 6.30 ml/kg. The normal probability plot of the data is linear with no gaps.
(a) What is the probability that a cardiac patient who regularly participates in sports has a maximum oxygen uptake of at least 20
ml/kg?
(b) If 10 cardiac patients are randomly selected, what is the probability they will have an average maximum oxygen uptake of at
least 20 ml/kg?
(c) If 40 cardiac patients are randomly selected, what is the probability they will have an average maximum oxygen uptake between
23 and 25 ml/kg?
Given the normal probability plot of total number of aircraft landings and takeoffs in a year (world’s 25 busiest airports) data. Assess
its normality. Explain your position.
5.
World's Busiest Airports
Normal Quantile Plot
Normal Quantile
2
1
0
-1
-2
100000
300000
500000
700000
900000
Number_of_landings_and_takeoffs
6.
Given the following statement: the percent of observations that are greater than z in a standard normal distribution is 8%. What zscore make the statement true?
A) – 3.14
B) – 2.41
C) – 1.41
D) 1.41 E) 2.41
F) 3.14
7.
A distribution of test scores is not symmetric. Which of the following is the best estimate of the z-score of the third quartile?
A) 0.67
B) 0.75
C) 1.00
D) 1.41
E) This z-score cannot be estimated from the information given.
8.
Population P1 and P2 are normally distributed and have identical means. However, the standard deviation of P1 is twice the standard
deviation of P2. What can be said about the percentage of observations falling within one standard deviation of the mean for each
population?
A) The percentage for P1 is twice the percentage for P2.
B) The percentage for P1 is greater, but not twice as great, as the percentage for P2.
C) The percentage for P2 is twice the percentage for P1.
D) The percentage for P2 is greater, but not twice as great, as the percentage for P1.
E) The percentages are identical.
9.
Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard deviation was 10.
On the second exam, the class mean was 70 and the standard deviation was 15. Lauren scored 85 on both exams. Assuming the
scores on each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class?
A) She scored much better on the first exam.
B) She scored much better on the second exam.
C) She scored about equally well on both exams.
D) It is impossible to tell because the class size is not given.
E) It is impossible to tell because the condition were not met.
10. In a certain southwestern city the air pollution index averages 62.5 during the year with a standard deviation of 18.0. Assuming that
the empirical rule is appropriate, the index falls within what interval about 95% of the time?
A) (8.5, 116.5)
B) (26.5, 98.5)
C) (26.5, 116.5)
D) (44.5, 80.5) E) (44.5, 98.5)
Ch 16 Probability Review with Vocabulary
Geometric setting
Binomial formula
Mean of binomial random variable
Geometric formula

Binomial setting
Calculator keystrokes for binomial formulas including cumulative distribution
Standard deviation of binomial r.v.
Calculator keystrokes for geometric formulas including cumulative distribution
10% of all TVs are defective. A quality control inspector randomly selects 5 TVs from the production line.
a) What is the probability that exactly one of these five TVs is defective?
b) What is the probability that at least 3 of these five TVs are defective?
c) What is the probability that the first defective TV is the fifth TV inspected?
d) What is the probability that there are some defective TVs among the 5 TVs inspected?
e) What is the probability that the first defective TV is within the first three TVs inspected?
f) What is the probability that there are no more than 3 defective TVs out of the 5 selected?
g) What is the expected number of defective TVs out of a sample of 5? And the standard deviation?
The army reports that the distribution of head circumference among soldiers is approximately normal with a mean 22.8 inches and
standard deviation 1.1 inches. Helmets are mass-produced for all except the smallest 5% and the largest 5% of head sizes. Soldiers in the
smallest or largest 5% get custom-made helmets.
a) What head sizes get custom-made helmets?
b) If twenty soldiers are currently ordering helmets, what is the probability that 2 are ordering custom-made helmets?
c) What percent of soldiers have a head circumference between 21.7 inches and 23.9 inches?
d) If soldiers are order helmets one at a time, what is the probability that the first soldier needing a custom-made helmet is the 5 soldier?
2007 B Free Response
The graph below display the relative frequency distribution for X, the total number of dogs and cats owned per household, for the
households in a large suburban area. For instance, 14 percent of the households own 2 of these pets.
a) According to a local law, each household in this area is prohibited from
owning more than 3 of these pets. If a household in this area is selected at
random, what is the probability that the selected household will be in
violation of this law? Show your work.
b) If 10 households in this area are selected at random, what is the probability that exactly 2 of them will be in violation of this law?
Show your work.
c) The mean and standard deviation of X are 1.65 and 1.851, respectively. Suppose 150 households in this area are to be selected at
random and X , the mean number of dogs and cats per household, is to be computed. Describe the sampling distribution of
its shape, center, and spread.
X , including