Download STAT-202, Basic Statistics Exam II

Exam II
Name:_____________________________ ______ I.D.:________________
Section I: Multiple-Choice
For each question in this section, circle the correct answer.
Questions 1-2 concern the following information:
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
1. The probability of assembling the product in 7 minutes or more is
(a) 0.25
(b) 0.75
(c) 1
(d) 0
2. The probability of assembling the product in 5 to 8 minutes is
(a) 0.50
(b) 0.75
(c) 0.25
(d) 0.30
3. A small school bus contains 8 1st-graders and 10 2nd-graders. If two children are ill,
what is the probability that at least one of them is a 2nd-grader?
(a) 28/153
(b) 125/153
(c) 16/153
(d) 27/306
4. An airplane is only allowed a gross passenger weight of 8000 kg. If the weights of
passengers traveling by air between Toronto and Vancouver have a mean of 78 kg
and a standard deviation of 7 kg, the approximate probability that the combined
weight of 100 passengers will exceed 8,000 kg is:
(a) 0.4978
(b) 0.3987
(c) 0.0044
(d) 0.0022
5. The central limit theorem states if the sample size n is large then
(a) The distribution of the sample data is approximately normal.
(b) The distribution of the sample mean is approximately standard normal.
(c) The distribution of the sample mean is approximately normal.
(d) The distribution of the population mean is approximately normal.
6. A random sample of 121 bottles of cologne showed an average content of 4 ounces. It
is known that the standard deviation of the contents (of the population) is 0.22
ounces. In this problem
1
(a)
(b)
(c)
(d)
0.22 is a parameter and 4 is a statistic.
4 is a parameter and 0.22 is a statistic.
4 and 0.22 are statistics.
4 and 0.22 are parameters.
7. In a large population of adults, the mean IQ is 112 with a standard deviation of 20.
Suppose 200 adults are randomly selected for a market research campaign. The
distribution of the sample mean IQ is
(a) Exactly normal with mean 112 and standard deviation 20.
(b) Approximately normal with mean 112 and standard deviation of 0.1.
(c) Approximately normal with mean 112 and standard deviation of 1.414.
(d) Approximately normal with mean 112 and standard deviation of 20.
8. The weights of extra large eggs have a normal distribution with a mean of 1 oz. and a
standard deviation of 0.1 oz. The probability that a dozen eggs weighs more than 13
oz. is closest to
(a)
(b)
(c)
(d)
0.0000
0.0020
0.1814
0.2033
9. On a December day, the probability of snow is 0.30. The probability of a "cold" day
is 0.50. The probability of snow and "cold" weather is 0.15. The events snow and
"cold" weather are
(a) Independent.
(b) disjoint.
(c) dependent.
(d) Independent only when they are also disjoint.
Questions 10-12 refer to the following information:
The student body of a large university consists of 60% female students. A random
sample of 8 students is selected.
10. What is the probability that among the students in the sample exactly two are female?
(a) 0.0896
(b) 0.2936
(c) 0.0413
(d) 0.0007
11. What is the probability that among the students in the sample at least 7 are female?
(a) 0.1064
(b) 0.0896
(c) 0.0168
(d) 0.8936
2
12. The mean and the variance of the female students in the sample are
(a) 4.8 and 1.92
(b) 3.2 and 1.92
(c) 4.8 and 1.39
(d) 3.2 and 1.39
14. The average hourly wage at a fast food restaurant is $5.85 with a standard deviation
of $0.35. Assume that the wages are normally distributed. The probability that the
average hourly wage of a sample of 25 workers is greater than $5.92 is
(a) 0.5793
(b) 0.4207
(c) 0.1587
(d) 0.8413
3
Question #1:
Twenty-five percent of the employees of a large company are minorities. A random
sample of 7 employees is selected.
a. What is the probability that the sample contains exactly 4 minorities?
b. What is the probability that the sample contains fewer than 2 minorities?
c. What is the probability that the sample contains exactly 1 non-minority?
d. What is the expected number of minorities in the sample?
e. What is the variance of the minorities?
4
Question #2:
You have two scales for measuring weights in a chemistry lab. Both scales give answers that
vary a bit in repeated weightings of the same item. If the true weight of a compound is 2 grams
(g), the first scale produces readings X that have mean 2.0 g and standard deviation .002 g. The
second scale produces readings Y that have mean 2.01 g and standard deviation .01 g.
(a) What are the mean and the standard deviation of the difference .5Y+2.2X? (The readings X
and Y are independent).
(b) You measure once with each scale and average the readings. Your result is Z = (X+Y)/2.
What are  z and  z ?
5
Question (3):
Suppose that the incomes in a population have mean $20,000 and standard deviation $3,500. A
sample of size 50 is selected.
(a) What is the probability that the sample mean will be within $3,000 of the population mean?
(b) Suppose that we want the probability of X being within $3,000 of the population mean to be
0.99. How large a sample do we need?
6