Download Answer: a) Quantitative ,ratio b) Quantitative, interval c) Categorical

Answer:
a) Quantitative ,ratio
b) Quantitative, interval
c) Categorical, ordinal
2. Fill in the
values in the table below to give a legitimate probability
distribution for the discrete random variable
,
,
, and
.
Value x of X
P(X=x)
-2
0.23
0
0.22
2
0.15
, whose possible values are
,
3
?
6
?
Answer:
Put 0.3 and 0.1
3. Let
be a random variable with the following probability distribution:
Value
Find the expectation
of
40
0.25
50
0.15
60
0.20
70
0.05
80
0.10
90
0.25
and variance
of
.
Answer:
E(x)=63.5
V(X)=372.75
4.
Let be a standard normal random variable. Calculate the following
probabilities using the calculator provided. Round your responses to at least
three decimal places.
P(Z> 1.62) = 0.053
P( Z lesser or equal to – 0.62)=0.268
P(1.15< Z< 1.85)=0.093
5. Let
be a standard normal random variable. Use the calculator provided to
determine the value of
such that
.
Carry your intermediate computations to at least four decimal places.
Round your answer to at least two decimal places.
Answer: -0.87
6. Suppose that the heights of adult women in the United States are
normally distributed with a mean of
inches. Jennifer is taller than
inches and a standard deviation of
of the population of U.S. women. How tall (in
inches) is Jennifer? Carry your intermediate computations to at least four decimal
places. Round your answer to at least one decimal place.
Answer: 67.1
7. An aptitude test is designed to measure leadership abilities of the test
subjects. Suppose that the scores on the test are normally distributed with a
mean of
and a standard deviation of
. The individuals who exceed
on this test are considered to be potential leaders. What proportion of the
population are considered to be potential leaders? Round your answer to at least
four decimal places.
Answer: 0.1492
8. Use the calculator provided to solve the following problems.

Consider a t distribution with
degrees of freedom. Compute
. Round your answer to at least three decimal
places.

Consider a t distribution with
such that
decimal places.
degrees of freedom. Find the value of
. Round your answer to at least three
P (-1.14 < t < 1.14) = 0.736
C= 1.706
9. Let
be a standard normal random variable. Use the calculator provided to
determine the value of
such that
.
Carry your intermediate computations to at least four decimal places.
Round your answer to at least two decimal places.
Answer: -0.63
10. According to records, the amount of precipitation in a certain city on a
November day has a mean of
inches, with a standard deviation of
inches. What is the probability that the mean daily precipitation will be
inches or more for a random sample of
November days (taken over many
years)? Carry your intermediate computations to at least four decimal places.
Round your answer to at least three decimal places.
Answer: 0.376
11.
In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who
were to be engaged in safety and security-related jobs, and found that 1,043 were
positive. (a) Construct a 95 percent confidence interval for the population proportion of
positive drug tests. (b) Why is the normality assumption not a problem, despite the very
small value of p? (Data are from Flying 120, no. 11 [November 1993], p. 31.)
12.
A random sample of 15 miniature Tootsie Rolls was taken from a bag. Each piece was
weighed on a very accurate scale. The results in grams were as given in the table at
right.
(a) Construct a 90 percent confidence interval for the true mean weight. (b) What
sample size would be necessary to estimate the true weight with an error of ± 0.02
grams with 90 percent confidence? (c) Discuss the factors which might cause variation
in the weight of Tootsie Rolls during manufacture.
X
3.087
3.131
3.241
3.241
3.270
3.353
3.400
3.400
3.408
3.411
3.435
3.437
3.437
3.439
3.477