University of Florida Exponential Distribution Standard Deviation Questions

QUESTION 1Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a
mean of $0.88. Suppose that we randomly pick 25 daytime statistics students.
Find the probability that an individual had between $0.80 and $1.00.
(Graph the situation, and shade in the area to be determined.)
Find the probability that the average of the 25 students was between $0.80 and $1.00.
(Graph the situation, and shade in the area to be determined.)
QUESTION 2
Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a
mean of $0.88. Suppose that we randomly pick 25 daytime statistics students.
What can you say about the probability that an individual had between $0.80 and $1.00 compared to the probability that the average of the
25 students was between $0.80 and $1.00.
a. The distributions are different. X is normal and
is exponential.
b. The distributions are the same. X is exponential and
c. The distributions are the same. X is normal and
is exponential.
is normal.
d. The distributions are different. X is exponential and
is normal.
QUESTION 3
Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed
with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students.
A. amount of change students carry
In words, Χ = ____________
Χ ~ _____(_____,_____)
In words,
= ____________
B. average amount of change carried by a sample of 25 students
C. N(0.88, 0.176)
D. E(0.88, 0.88)
~ ______ (______, ______)
QUESTION 4
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. We randomly sample 49 fly balls.
What is the probability that the 49 balls traveled an average of less than 240 feet?
(Sketch the graph. Scale the horizontal axis for X . Shade the region corresponding to the probability. Find the probability.)
Find the 80th percentile of the distribution of the average of 49 fly balls.
QUESTION 5
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. We randomly sample 49 fly balls.
If
= average distance in feet for 49 fly balls, then
a. N(250,
)
b. N(250,
c. N(
d. N(250,
)
, 250)
)
~ _______(_______,_______)
QUESTION 6
Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard
deviation of 14 minutes. Consider 49 of the races. Let
the average of the 49 races.
A. N(145,
~ _____(_____,_____)
Find the probability that the runner will average
between 142 and 146 minutes in these 49
marathons.
B. 0.6247
Find the 80th percentile for the average of these 49
marathons.
E. 147.23
Find the median of the average running times.
G. 146
C. N(145,
)
)
D. 145
F. 0.5762
H. 146.68
QUESTION 7
In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38
farmers from 1940.
~ _____(_____,_____)
a. N(
, 174)
b. N(174,
)
c. N(174,
d. N(
)
, 174)
QUESTION 8
In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38
farmers from 1940.
The IQR for X is from
acres to
acres.
QUESTION 9
In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38
farmers from 1940.
In words, Χ = ____________.
In words, = ___________.
a. Χ = the average size of a U.S. farm in 1940
= the average size of a U.S. farm as estimated from a sample of 38, in acres
b. Χ = the size of a U.S. farm in 1940
= the average size of a U.S. farm as estimated from a sample of 38, in acres
c. Χ = the average size of a U.S. farm as estimated from a sample of 38, in acres
= the size of a U.S. farm in 1940
d. Χ = the size of a U.S. farm in 1940, in acres
= the sizes of U.S. farms estimated from a sample of 38 farms
QUESTION 10
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard
deviation of about ten. Suppose that 16 individuals are randomly chosen. Let = average percent of fat calories.
For the group of 16, find the probability that the average percent of fat calories consumed is more than five.
(Graph the situation and shade in the area to be determined.)
Find the first quartile for the average percent of fat calories.
QUESTION 11
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard
deviation of about ten. Suppose that 16 individuals are randomly chosen. Let
~ ______(______, ______).
a. N(36,
)
b. N(
,
c. N(
, 36)
d. N(36,
)
)
QUESTION 12
Which of the following is NOT TRUE about the distribution for averages?
a. The mean, median, and mode are equal.
b. The curve is skewed to the right.
c. The area under the curve is one.
d. The curve never touches the x-axis.
= average percent of fat calories.