University of Florida Median and Probability Worksheet

QUESTION 1The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.
What is the median recovery time?
a. 7.4
b. 2.1
c. 2.7
d. 5.3
QUESTION 2
The length of time to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two
minutes. If the mean is significantly greater than the standard deviation, which of the following statements is true?
I. The data cannot follow the uniform distribution.
II. The data cannot follow the exponential distribution.
III. The data cannot follow the normal distribution.
a. I only
b. II only
c. III only
d. I, II, and III
QUESTION 3
The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean µ = 125 and standard deviation
σ = 14. Systolic blood pressure for males follows a normal distribution.
Calculate the z-scores for the male systolic blood pressures 100 and 150 millimeters.
z-score for 100 =
z-score for 150 =
QUESTION 4
The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean µ = 125 and standard deviation
σ = 14. Systolic blood pressure for males follows a normal distribution.
If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood
pressure was between 100 and 150 millimeters, what would you say to him?
a. I would tell him that 2.5 standard deviations below the mean would give him a blood pressure reading of 110, which is in the range of 100 to
150.
b. I would tell him that 2.5 standard deviations below the mean would give him a blood pressure reading of 160, which is above the range of
100 to 150.
c. I would tell him that 2.5 standard deviations below the mean would give him a blood pressure reading of 90, which is below the range of 100
to 150.
d. I would tell him that 2.5 standard deviations below the mean would give him a blood pressure reading of 70, which is below the range of 100
to 150.
QUESTION 5
Height and weight are two measurements used to track a child’s development. The World Health Organization measures child development by
comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80 cm girls in the reference population had
a mean µ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N (10.2, 0.8).
Calculate the z-scores that correspond to the following weights and interpret them:
11 kg
A child who weighs 11 kg is
standard deviation(s) (above/below)
the mean of 10.2 kg.
7.9 kg
A child who weighs 7.9 kg is
standard deviation(s) (above/below)
the mean of 10.2 kg.
12.2 kg
A child who weighs 12.2 kg is
standard deviation(s) (above/below)
the mean of 10.2 kg.
QUESTION 6
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.
What is the probability of spending more than two days in recovery?
a. 0.9420
b. 0.0553
c. 0.0580
d. 0.8447
QUESTION 7
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two
minutes.
Based upon the given information and numerically justified, would you be surprised if it took less than one minute to find a parking space?
a. Yes.
b. No.
c. Unable to determine.
QUESTION 8
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two
minutes.
Seventy percent of the time, it takes more than how many minutes to find a parking space?
a. 6.05
b. 1.24
c. 2.41
d. 3.95
QUESTION 9
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an
individual.
X ~ ____(____,____)
A. The probability that a person has an IQ greater than 120 is 0.0918.
B. The middle 50% of IQ scores falls between 87.05 and 112.95.
Find the probability that the person has an IQ greater
C. The middle 50% of IQ scores falls between 89.95 and 110.05.
than 120. Write a probability statement.
MENSA is an organization whose members have the D. N(100, 15)
top 2% of all IQs. Find the minimum IQ needed to
E. B(15,100)
qualify for the MENSA organization. Write the
F. A person has to have an IQ over 130 to qualify for MENSA.
probability statement.
The middle 50% of IQs fall between what two values? G. A person has to have an IQ over 125 to qualify for MENSA.
Write the probability statement.
H. The probability that a person has an IQ greater than 120 is 0.0632.
QUESTION 10
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50
feet.
If X = distance in feet for a fly ball, then X ~
(
,
)
If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220
feet?
(Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.)
Find the 80th percentile of the distribution of fly balls:
(Sketch the graph, and write the probability statement.)
Eighty percent of the fly balls will travel (less/greater)
than
feet.
QUESTION 11
In the 1992 presidential election, Alaska’s 40 election districts averaged 1,956.8 votes per district for President Clinton. The standard deviation
was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X =
number of votes for President Clinton for an election district.
State the approximate distribution of X.
X ~ N(
,
)
Is 1,956.8 a population mean or a sample mean?
(population/sample)
Find the probability that a randomly selected district had fewer than 1,600 votes for President Clinton.
(Sketch the graph and write the probability statement.)
The probability that a district had less than 1,600 votes for President Clinton is
.
Find the probability that a randomly selected district had between 1,800 and 2,000 votes for President Clinton.
Find the third quartile for votes for President Clinton.
Seventy-five percent of the districts had (more/fewer)
than
votes for President Clinton.
QUESTION 12
Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28
seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.
In words, define the random variable X.
X ~ _____(_____,_____)
A. X ~ N(2.28,129.71)
B. 125.42
C. 125.19, 131.41
Find the percent of her laps that are completed in less
D. 64.34%
than 130 seconds.
E. X ~ N(129.71, 2.28)
The fastest 3% of her laps are under _____.
F. 126.79, 132.63
The middle 80% of her laps are from _______ seconds
G. X = the distribution of race times that Terry Vogel produces
to _______ seconds.
H. 55.17%
I. X = the distribution of laps that Terry Vogel races
J. 127.63
QUESTION 13
An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard
deviation of 13 days. An alleged father was out of the country from 240 to 306 days before the birth of the child, so the pregnancy would have
been less than 240 days or more than 306 days long if he was the father. The birth was uncomplicated, and the child needed no medical
intervention.
What is the probability that he was NOT the father?
What is the probability that he could be the father?
(Calculate the z-scores first, and then use those to calculate the probability.)
z-score for x = 240 =
z- score for x = 306 =
P(NOT the father) =
P(father) =
QUESTION 14
We flip a coin 100 times (n = 100) and note that it only comes up heads 20% (p = 0.20) of the time. The mean and standard deviation for the
number of times the coin lands on heads is μ = 20 and σ = 4 (verify the mean and standard deviation). Solve the following:
There is about a 68% chance that the number of
heads will be somewhere between ___ and ___.
A. 92.63%
B. 12 and 26.
There is about a ____chance that the number of heads C.
99.73%
will be somewhere between 12 and 28.
D. 95%
There is about a ____ chance that the number of
E. 85.75%
heads will be somewhere between eight and 32.
F. 16 and 24.
QUESTION 15
Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site. On average, 28 percent of 18 to 34 year
olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard
deviation of five percent.
Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30.
Find the 95th percentile, and express it in a sentence.
95% of 18 to 34 year olds who check Facebook before getting out of bed in the morning is at (most/least)
%.