Download Matt Jones Math 1530: Elements of Statistics Exam II, VERSION 4

Matt Jones
Math 1530: Elements of Statistics
Exam II, VERSION 4
NAME:
INSTRUCTIONS:
Take the class period to complete this exam. You may use a calculator, a writing utensil,
one page of notes, normal tables, and your brain. Do not share any materials and you must
do your own work to receive any credit. Round all final answers at the fourth decimal place
(the ten-thousandth’s place). Good luck!
1. [4 POINTS] Shade the appropriate regions in the following Venn diagrams:
A∪B
A∪B
2. [2 POINTS] How many different ways could you select 4 DVDs to rent if there are 25 to choose
from?
3. [2 POINTS] How many ways can you choose 4 DVDs from 25 and watch them in order?
4. [2 POINTS] How many ways could you watch 8 DVDs in order?
5. [4 POINTS] Some results of a recent poll on funding local road projects are below:
Response
Frequency
Increase spending
548
Decrease spending
194
Spend the same as last year
90
No opinion
441
(a) What is the probability that a person chosen at random from this group responded “Spend the
same as last year” or “No opinion”?
(b) What is the probability that a person chosen at random responded “Decrease spending”?
6. [6 POINTS] Suppose X has a normal distribution with mean 87 and standard deviation 3.1.
Calculate
(a) P (X > 90).
(b) Calculate P (86 ≤ X ≤ 91).
(c) If a random sample of size 12 is taken from this distribution, what is the chance its mean will
be more than 2 from 87? That is, what is P (|X − 87| > 2)?
7. [4 POINTS] What is the approximate distribution of the mean of a random sample of size 150 from
a population whose mean and standard deviation are 22 and 10, respectively?
8. [2 POINTS] Calculate
(a) z0.09
(b) z0.65
9. [4 POINTS] The eye pressures for Caucasians and African Americans are about the same, and are
distributed approximately normal with mean 15.5 mmHg and standard deviation 2 mmHg. What is
the 75th percentile?
10. [2 POINTS] Consider the following normal probability plots for three data sets.
Which answer (a, b, c, d, or e) is the most appropriate?
Answer
a
b
c
d
e
Could be normally distributed
Set 1 Set 1 Set 2 Set 2 Set 3
Probably not normally distributed Set 2 Set 3 Set 1 Set 3 Set 2
Difficult to tell
Set 3 Set 2 Set 3 Set 1 Set 1
11. [10 POINTS]Suppose 7% of all widgets have tapers. Scotty chooses 15 widgets at random. Calculate
(a) the probability that exactly 2 of the 15 widgets have tapers.
(b) the probability that at least 1 of the 15 widgets have tapers.
(c) the expected number of the 15 widgets that have tapers.
(d) the standard deviation of the number of the 15 widgets that have tapers.
(e) If Scotty takes a sample of 200 widgets, the number having tapers will be distributed
i.
ii.
iii.
iv.
v.
approximately
approximately
approximately
approximately
approximately
normal with mean 15.
binomial with mean 15.
normal with mean 14.
normal with mean 7.
binomial with mean 7.
12. [8 POINTS] The numbers of siblings for a group of people are represented in the histogram below.
(a) What is the probability a person chosen at random from this group had at least two siblings?
(b) What proportion of these people had no siblings?
(c) What is the average number of siblings per person for this group?
(d) What is the standard deviation of siblings per person for this group?