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Question: 1.
In a large population of adults the mean IQ is 112 with a standard deviation of 20. There were 200 were randomly selected for research. Find the probability that the sample mean IQ is greater than 110. (1 point)

0.092
0.438
0.579
0.760
0.921

2.
Let the random variable X be the outcome of rolling a 6-sided die. Assuming the die is fair, the probability distribution is as follows:

X 1 2 3 4 5 6
Probability 1/6 1/6 1/6 1/6 1/6 1/6


What is the variance of X? (1 point)

2.92
1
1.75
1/6
2.39

3.
In a large population of high school students, 20% have experienced math anxiety. You take a random sample of 10 students from this population. The standard deviation of the number of students in the sample who have experienced math anxiety is ____. (1 point)

0.0160
0.2070
0.2530
1.0000
1.2650

4.
A factory makes processors for use in computers. It is known that about 90% of the processors meet specifications. Every week a sample of 18 processors is selected at random for testing. Assume a binomial distribution is valid. Suppose you collect a large number of these samples of 18 processors and determine the number meeting specifications in each sample. What is the mean number of processors meeting specifications? (1 point)

1.62
16.2
4.02
16
22.3

5.
A hospital has three emergency power generators that operate when there is a power outage. The probability that a generator fails to operate is 0.2 and the three generators are independent. What is the probability that none of the generators operate properly during a power outage? (1 point)

0.008
0.512
0.06
0.6
0.488

Essay
Your teacher will grade your response to ensure you receive proper credit for your answer.
6.
A coin is unbalanced such that it comes up tails 55% of the time.

a) What is the probability that you don't flip a head until the fourth flip?
b) What is the probability that you don't flip a tail until the fourth flip?
c) How many tosses would it take, on average, to flip a head?
d) How many tosses would it take, on average, to flip a tail? (4 points)
7.
A coin is unbalanced such that it comes up tails 55% of the time. In an effort to prove that the coin is unfair, an experimenter flips the coin 50 times.

a) What is the probability that the coin comes up tails more than 25 times?
b) What is the probability that the coin comes up tails more than 30 times?
c) What is the probability that the coin comes up tails exactly 25 times? (4 points)
8.
According to government data, 15% of employed women have never been married. Take a random sample of employed women and observe their marital status.

a) Is X normal, binomial, or geometric?
b) If 8 employed women are selected at random, what is the probability that 2 or fewer have never been married?
c) If 8 employed women are selected at random, what are the mean and standard deviation? (4 points)
9.
In a game of dice, you roll two standard six-sided dice and examine their sum.

a) What is the probability of rolling a 7?
b) If you roll the dice 20 times, what is the probability of rolling a total of 3 sums of 7?
c) How many times would you expect to roll the dice before you rolled a sum of 12? (4 points)
Essay
Your teacher will grade your response to ensure you receive proper credit for your answer.
10.
A can of Pepsi is supposed to contain, on the average, 12 ounces of soda with a standard deviation of 0.3 ounces. Suspecting fraud, you take a random sample of 40 cans and measure the amount of Pepsi in each. Your measurements show that the 40 cans had a mean of 11.9 ounces. What is the probability of a random sample of 40 cans having a mean of 11.9 ounces of soda or less?   Edit

Answer:
1. Need to find P(x-bar > 110) = ?

z = (110 - 112)/(20/sqrt(200))
= -1.4142

P(x-bar > 110) = P(z > -1.4142)
= 0.9213 (Ans.)  Edit

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