Online 09 - Section 6.2-Doug Ensley
Student: _____________________
Date: _____________________
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Instructor: Doug Ensley
Course: MAT117 01 Applied Statistics Ensley
Assignment: Online 09 - Section 6.2
1. In January 2011, the average monthly rental rate for one-bedroom apartments in a certain city was $811. Suppose rental
rates across all one-bedroom apartments in this city follow approximately a normal distribution, with a standard deviation of
$160. Find the approximate proportion of one-bedroom apartments for which the rental rate:
a. is at least $1000 a month.
b. is less than $500 a month.
c. is between $500 and $1000 a month.
a. The proportion of apartments with rent that is at least $1000 a month is
.
(Round to four decimal places as needed.)
b. The proportion of apartments with rent less than $500 a month is
.
(Round to four decimal places as needed.)
c. The proportion of apartments with rent between $500 and $1000 a month is
.
(Round to four decimal places as needed.)
2. A new roller coaster at an amusement park requires individuals to be at least 4' 8" (56 inches) tall to ride. It is estimated
that the heights of 10-year-old boys are normally distributed with μ = 53.5 inches and σ = 5 inches.
a. What proportion of 10-year-old boys is tall enough to ride the coaster?
b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10-year-old boys is tall enough to
ride this coaster?
c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in
part a?
a. The proportion of 10-year-old boys tall enough to ride the coaster is
.
(Round to four decimal places as needed.)
b. The proportion of 10 year-old-boys tall enough to ride the smaller coaster is
.
(Round to four decimal places as needed.)
c. The proportion of 10-year-old boys tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a
is
.
(Round to four decimal places as needed.)
3. For one test's distribution (μ = 386, σ = 109) and another test's distribution (μ = 24, σ = 5) which score is relatively higher, a
score of 672 on the first test or a score of 26 on the second test? Explain.
Select the most appropriate answer from those below.
A. The first score is relatively higher than the second score because the z-score of the score on
the first test is equal to the z-score of the score on the second test.
B. The test scores are equally high because the z-score of the score on the first test is equal to
the z-score of the score on the second test.
C. The first score is relatively higher than the second score because the z-score of the score on
the first test is greater than the z-score of the score on the second test.
D. The second score is relatively higher than the first score because the z-score of the score on
the first test is less than the z-score of the score on the second test.
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4. In January 2011, the average monthly rental rate for one-bedroom apartments in a certain city was $758. Suppose rental
rates across all one-bedroom apartments in this city follow approximately a normal distribution, with a standard deviation of
$180. Find the approximate proportion of one-bedroom apartments for which the rental rate:
a. is at least $1000 a month.
b. is less than $500 a month.
c. is between $500 and $1000 a month.
a. The proportion of apartments with rent that is at least $1000 a month is
.
(Round to four decimal places as needed.)
b. The proportion of apartments with rent less than $500 a month is
.
(Round to four decimal places as needed.)
c. The proportion of apartments with rent between $500 and $1000 a month is
.
(Round to four decimal places as needed.)
5. A new roller coaster at an amusement park requires individuals to be at least 4' 8" (56 inches) tall to ride. It is estimated
that the heights of 10-year-old boys are normally distributed with μ = 53.5 inches and σ = 4 inches.
a. What proportion of 10-year-old boys is tall enough to ride the coaster?
b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10-year-old boys is tall enough to
ride this coaster?
c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in
part a?
a. The proportion of 10-year-old boys tall enough to ride the coaster is
.
(Round to four decimal places as needed.)
b. The proportion of 10 year-old-boys tall enough to ride the smaller coaster is
.
(Round to four decimal places as needed.)
c. The proportion of 10-year-old boys tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a
is
.
(Round to four decimal places as needed.)
6. A health study reported that, in one country, systolic blood pressure readings have a mean of 124 and a standard deviation
of 13. A reading above 140 is considered to be high blood pressure. Complete parts a through d below.
a. What is the z-score for a blood pressure reading of 140?
z=
(Round to two decimal places as needed.)
b. If systolic blood pressure in that country has a normal distribution, what proportion of the population suffers from high
blood pressure?
The proportion with high blood pressure is
.
(Round to four decimal places as needed.)
c. What proportion of the population has systolic blood pressure in the range from 102 to 140?
The proportion with systolic blood pressure between 102 and 140 is
.
(Round to four decimal places as needed.)
d. Find the 90th percentile of blood pressure readings.
The 90th percentile of blood pressure readings is
.
(Round to the nearest whole number as needed.)
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7. An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 95 and
a standard deviation of 12. Answer the questions below.
Click here to view page 1 of the standard normal table.1
Click here to view page 2 of the standard normal table.2
a. What proportion of children have an index of (i) at least 119? (ii) at least 74?
(i) The proportion of children having an index of at least 119 is
.
(Round to four decimal places as needed.)
(ii) The proportion of children having an index of at least 74 is
.
(Round to four decimal places as needed.)
b. Find the index score that is the 93rd percentile.
The 93rd percentile index score is
.
(Round to two decimal places as needed.)
c. Find the index score such that only 7% of the population has an index below it.
7% of the population have an index score below
.
(Round to two decimal places as needed.)
1: Standard normal table
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2: Standard normal table
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Online 09 - Section 6.2-Doug Ensley
1.
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0.1188
0.0260
0.8553
2.
0.3085
0.7580
0.4495
3.
C.
The first score is relatively higher than the second score because the z-score of the score on the first test is greater than the
z-score of the score on the second test.
4.
0.0894
0.0759
0.8347
5.
0.2660
0.8092
0.5432
6.
1.23
0.1092
0.8455
141
7.
0.0228
0.9599
112.76
77.24
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