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Quiz 12 Review
Name:
Standard(s) assessed
Score
Using the binomial distribution

Graph a binomial distribution

Compute probabilities based on a binomial distribution
Using Normal Distributions

Sketch the graph of a normal distribution

calculate z-scores

Calculate probabilities/proportions pertaining to a normal distribution

Calculate values of a variable corresponding to given probabilities or proportions
Binomial Distribution
The probability of k successes in n trials where p is the probability if success on each trial is
given by the formula:
k
nk
n Ck p (1 p)
1.
2.
Show the formula used with the substitution for all problems.
Suppose the Phillies have a .7 probability of beating the Mets for each game and that they
will play the Mets 4 times. Calculate the following probabilities
a.
P(4 wins)
b.
P(2 wins)
c.
P(0 wins)
d.
P(at least 1 win)
A basketball player has made 80% of her free throws over a long season. At the end of
the tournament she attempts 5 free throws and only makes 2. The fans say she “choked”
under pressure; however, her 2 out of 5 free throws could be the result of random
variation or chance. Viewing the problem as a binomial experiment, calculate the
probability that she will make only 2 or fewer out of 5 free throws.
Normal Distributions
3.
Compute the z-score for a score of 78 on a test with the following summary statistics:
min = 20, Q1 =70, med = 75, Q3 = 76, max = 100, s = 4, x = 70
(a) z = -2
(b) z = 2.5
(c) z = 0
(d) z = 7
(e) none of these
4.
On a Science test 3 students in a large class earned scores resulting in the z-scores below.
Explain briefly how each student did relative to the rest of the class.
5.
a.
z = -2.81
b.
z = .07
c.
z = 1.2
The height of American adult males is normally distributed with a mean of 70 inches
and a standard deviation of 3 inches.
a.
Sketch the normal distribution described above labeling the mean and standard
deviation, and shade in the proportion associated with b.
b.
Calculate the probability of a randomly selected adult male being taller than 76
inches.
c.
What proportion of adult males are less than 6 feet tall?
d.
What proportion of adult males are between 66 and 74 inches tall?
e.
What height is the 75 percentile for adult males?

6.
7.
If a set of test scores are normally distributed with a mean of 75 and a standard deviation
of 15 compute the following…
a. The probability of a randomly selected student scoring above 90 is
_______.
b. The proportion of students scoring between 60 and 80 is
_______.
c. Only 5% of students scored above what score?
_______.
Open “Heights.txt” in StatCrunch. This data set contains the heights in cm for 507 adults.
Create a histogram and note that the data are approximately normal.
Compute the mean and standard deviation.
Using the normal distribution and the computed mean and standard deviation,
approximate the proportion of people shorter than 165 cm.
Compare this number to the actual proportion of people shorter than 165 cm.