Math 2311 EMCF Homework 5Sections 4.3 - 4.4Honework will NOT be accepted through email or in person. Homework must be su...

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Math 2311 EMCF Homework 5

April 14, 2018

Math 2311 EMCF Homework 5
Sections 4.3 - 4.4
Honework will NOT be accepted through email or in person. Homework must be submitted through
CourseWare, https://www.casa.uh.edu, before the deadline. Submit this assignment on CourseWare under
“EMCF” and choose ehw5.

1. True or False: On a statistics exam, Joe’s score was at the 20th percentile and John’s score was at the
40th percentile, thus, we can say that John’s score was twice Joe’s.
a. True
b. False
2. True or False: On the normal curve, the 50th percentile corresponds to the mean.
a. True
b. False
3. If a distribution has a mean of 48 and standard deviation of 3.2, what is the value that corresponds to
a z-score of -1.6?
a.
b.
c.
d.
e.

38.22
42.88
53.12
46.40
none of these

4. Find P (?1.2 < Z < 1.9)
a.
b.
c.
d.
e.

0.9713
0.8562
0.8020
0.7659
none of these

5. Find c such that P (Z > c) = 0.3859
a.
b.
c.
d.
e.

-0.29
0.35
-0.35
0.29
none of these

1

0.04
0.00

density

0.08

Use the following to answer questions 6 - 10: The following is the Normal density curve for the MPG of a
large sedan with a mean of 26.5 mpg and standard deviation 3.7.

15.4

19.1

22.8

26.5

30.2

33.9

6. What proportion of large sedans have a MPG of less than 25.5 mpg?
a.
b.
c.
d.
e.

27%
39.35%
-39.35%
-27%
none of these above

7. What is the probability that a sedan has a MPG greater than 30.5 mpg?
a.
b.
c.
d.
e.

0.86
1.08
0.14
0
none of these above

8. What is the probability that a sedan has between 25.5 and 30.5 mpg?
a.
b.
c.
d.
e.

0.95
0.2535
0.3935
0
none of these above

2

37.6

9. What is the 90th percentile of the MPG of these sedans?
a.
b.
c.
d.
e.

23.85
2.65
31.24
0
none of these above

10. Give the first quartile (Q1 )of the MPG of these large sedans.
a.
b.
c.
d.
e.

6.625
24
29
27.425
none of these above

11. The sampling distributon of a statistic is
a.
b.
c.
d.
e.

The probability that we obtain the statistic in repeated random samples.
The mechanism that determines whether randomization was effective.
The distribution of values taken by a statistic in all possible samples of the same sample size.
The extent to which the sample results differ systematically from the truth.
none of these

Use the following to answer questions 12 - 13: The high temperature in Chicago for the month of August is
approximately normally distributed with mean µ = 80? F and standard deviation ? = 8? F. Suppose we take
a SRS of 16 days in August and want to determine the sample mean, x
¯ high temperature.
12. What is the standard deviation (standard error) of the sample mean high temperature.
a.
b.
c.
d.
e.

8
2
0.5
10
20

13. What is the probability that a random sample of 16 days in August have a sample mean high temperature
of at least 82? F?
a.
b.
c.
d.
e.

0.5987
0.2500
0.1587
0.8413
Cannot be determined.

3

14. The expected value of the sampling distribution of the sample mean is equal to
a.
b.
c.
d.
e.

the standard deviation of the sampling population
the mean of the sampling population
the median of the sampling population
the population size
none of these

15. Power companies kill trees growing near their lines to avoid power failures due to falling limbs in
storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the chemical
kills some of the trees. Suppose that one such chemical would kill 15% of sycamore trees. The power
company tests the chemical on 200 sycamores. Consider these a SRS from the population of all sycamore
trees. What is the probability that no more than 32 trees are killed?
a.
b.
c.
d.
e.

0.0571
0.6540
0.3460
0.1598
none of these

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