Stat 511 Sample Multiple Choice Questions

Stat 511
Sample Multiple Choice Questions
1. If the probability density function of a continuous random variable X is
.5 x
f ( x)  
0
0 x2
otherwise
then, P(1  x  1.5) is
A.
B.
C.
D.
.5625
.3125
.1250
.4375
2. If the probability density function of a continuous random variable X is
kx 2

f ( x)  

0
0 x2
otherwise
then the value of k is
A.
B.
C.
D.
2
.25
.375
any positive value greater than 2
3. A continuous random variable X is uniformly distributed over the interval [10, 16]. The expected
value of X is
A.
B.
C.
D.
16
13
10
7
4. Which of the following statements are correct?
A. If the random variable X is normally distributed with parameters  and  , then the mean
of X is  and the variance of X is  .
B. The cumulative distribution function of any standard normal random variable Z is
P(Z  z )  ( z ).
C. The standard normal distribution does frequently serve as a model for a naturally arising
population.
D. The standard normal probability table can only be used to compute probabilities for normal
random variables with parameters   0 and   1.
E. All of the above statements are correct.
5. If X is a normally distributed random variable with a mean of 80 and a standard deviation of 12,
then the P(X = 68) is
A.
B.
C.
D.
E.
.1587
.0000
.6587
.8413
None of the above answers are correct
6. A function p(x,y) of two discrete random variables X and Y can be used as a joint probability
mass function provided that:
A. p( x, y)  0 x and y
B.   p( x, y)  1
x
y
C. Both A and B are required conditions
D. Either A or B is a required condition
7. If X and Y are independent random variables with
pX (0)  .5, pX (1)  .3, pX (2)  .2 and pY (0)  .6, pY (1)  .1, pY (2)  .25, and pY (3)  .05. Then P( X  1 and Y  1) is
A.
B.
C.
D.
.30
.56
.70
.80
8. If  is the correlation coefficient between two variables X and Y, then which of the following
statements are correct?
A. A value of  less than 1 in absolute value indicates only that the relationship is not
completely linear, but there may still be a very strong nonlinear relationship.
B.   0 does not imply that X and Y are independent, but there is complete absence of a linear
relationship.
C. When   0 , X and Y are said to be uncorrelated.
D. The variables X and Y could be uncorrelated yet highly dependent because there is a strong
nonlinear relationship.
E. All of the above are correct statements
9. The sampling distribution of X appears below:
x
10
15
p(
.25
.30
x)
Then, the expected value of X ; E ( X ) is
20
010
25
.35
A.
B.
C.
D.
E.
17.75
17.50
4.183
4.213
None of the above answers is correct
10. Which of the following statements are true if X1 , X 2 ,
distribution with mean  ?
, X n is a random sample from a
E. The sample mean X is always an unbiased estimator of  .
F. The sample mean  is an unbiased estimator of  if the distribution is continuous and
symmetric.
G. Any trimmed mean is an unbiased estimator of  if the distribution is continuous and
symmetric.
H. None of the above statements are true.
I. All of the above statements are true.
11. The assembly time for a product is uniformly distributed between 6 to 10 minutes. The
probability of assembling the product in 5 to 8 minutes is
A.
B.
C.
D.
0.50
0.75
0.25
0.30
12. 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.
B.
C.
D.
Exactly normal with mean 112 and standard deviation 20.
Approximately normal with mean 112 and standard deviation of 0.1.
Approximately normal with mean 112 and standard deviation of 1.414.
Approximately normal with mean 112 and standard deviation of 20.
13. When figure skaters need to find a partner for “pair figure skating," it is important to find a
partner who is compatible in weight. The weight of figure skaters can be modeled by a normal
distribution. For male skaters, the mean is 170 lbs. with a standard deviation of 10 lbs. For
female skaters, the mean is 110 lbs. with a standard deviation of 5 lbs. Let the random variable X
= the weight of female skaters and the random variable Y = the weight of male skaters. The
weight of a pair of figure skaters (a male and a female) can be thought of as a new random
variable. Let the random variable W = X + Y. What is the mean of this new random variable W?
A.
B.
C.
D.
110 lbs.
140 lbs.
170 lbs.
280 lbs.