Download MATH 156, General Statistics

MATH 156, General Statistics
Test 2
Peck, Olsen & Devore, Ch. 6-8
February 27, 2003
Name_____________________________________
1. Automobiles arriving at an intersection have three choices: turn right (R), turn left
(L), or go straight (S).
a) Give the sample space for all possibilities for the next two cars at the
intersection. (e.g. the event that the first goes left and the second right
could be written LR).
b) Which outcomes make up the event that both go the same way?
c) Which outcomes have at least one car going straight?
d) If all the outcomes are equally likely, find the probabilities for the events
in part b)_________ and part c)___________.
2. On a roulette wheel, there are 38 slots marked 0, 00, 1, 2, 3,…,, 36. The numbers
0 and 00 are green, while the other even numbers are black and the odd numbers
are red. Each slot is just as likely to contain the ball as each other slot. Find the
probability that the ball winds up on a slot that is:
a) green _______ b) either red or green _______ c) not green ________.
3. The test light on a CO detector flashes every 30 seconds to indicate that the
device is working. If you arrive at the detector at a random time, find the
probability that the time you have to wait to observe the flash is:
a) less than 10 seconds______ b) more than 10 seconds _______
c) between 10 and 20 seconds _______ d) at least 10 seconds__________
MATH 156, Test 2, 2/27/03, page 2
4. The probability distribution for the number of spades selected in a sample of four
taken with replacement is given below.
X
0
1
2
3
4
P(X)
81/256
108/256
?
12/256
1/256
a) Find P(2)________________
b) the mean ________________
c) the standard deviation ________.
5. Suppose that the heights of adult Americans are normally distributed with mean
170 cm. and standard deviation 10 cm. Find the probability that the height of a
randomly selected individual from the population is:
a) between 150 and 190 cm.__________ b) above 160 ____________
c) less than 150 _____________
d) no more than 150 ___________.
6. Using the information in problem 5, just 5% of adult Americans are taller than
what height? ____________, only 10 % are shorter than what
height?_____________
7. Suppose a sample of 16 individuals is taken from the population in problem 5.
a) What can be said about the probability distribution for , the sample
mean? Justify your answer.
b) Find the probability that the sample mean is between 165 and 180.
c) Find the probability that the sample mean is greater than 175.
d) Find the mean height exceeded only 2% of the time.
MATH 156, Test 2, 2/27/03, page 3
8. Suppose the wait for a subway train is between 0 and 12 minutes with all times
equally likely. Such a distribution has mean 6 and standard deviation of 3.5 a
commuter takes a random sample of 49 of her waiting times and computes the
mean, .
a. Find the mean value for the population of all such means, .
b. Find the standard deviation for the population of such means.
c. What, if anything, can be said about the probability distribution of such
means? Justify your answer.
9. A salesperson is successful on 75% of his calls. Let p be the proportion of
successes in a sample of 48 calls.
a. Find the mean of the population of all such sample proportions, p.
b. Find the standard deviation for those proportions, p.
c. An analyst claims that a normal distribution can be used to get
probabilities for various values of p. Do you agree? Why or why not?
10. What is the smallest sample size that one can use to justify use of the normal
distribution in problem 9?