Stats Exam #2

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.5?

0.0000

A production process has been producing 10% defective items. A sample of three items is selected from the production process. What is the probability that all three items are defective?

0.001

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that X is greater than 10.52 is

0.0029

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

0.0142

If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪ B) = 0.88, then P(B | A) =

0.04

If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A | B) =

0.05

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Refer to Exhibit 5-4. The probability that there are no females in the sample is

0.0778

The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 7 are female?

0.1064

Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. The probability density function has what value in the interval between 20 and 28?

0.125

If a coin is tossed three times, the likelihood of obtaining three heads in a row is

0.125

f(x) =(1/10) e-x/10 x ≥ 0 The probability that x is between 3 and 6 is

0.1920

If P(A) = 0.48, P(A ∪ B) = 0.82, and P(B) = 0.54, then P(A ∩ B) =

0.2000

The probability density function for a uniform distribution ranging between 2 and 6 is

0.25

f(x) =(1/10)e^-x/10 x ≥ 0 The probability that x is less than 5 is

0.3935

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

0.43

For a standard normal distribution, the probability of z ≤ 0 is

0.5

The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. Computers with prices of more than $1,750 receive a discount. What percentageof the computers will receive the discount?

0.62%

Z is a standard normal random variable. The P(-1.5 ≤ Z ≤ 1.09) equals

0.7953

Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. Then, P(Bc) =

0.8

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

24

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.

5.3

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Refer to Exhibit 6-8. What percentage of tires will have a life of 34,000 to 46,000 miles?

76.98%

A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?

8.53%

Which of the following is not a characteristic of the normal probability distribution?

99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-8. The random variable x satisfies which of the following Discrete Probability Distributions?

Poisson

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a

Poisson distribution

Which of the following statements about a discrete random variable and its probability distribution are true?

Values of f(x) must be greater than or equal to zero.

The exponential probability distribution is used with

a continuous random variable

In statistical experiments, each time the experiment is repeated

a different outcome may occur

The number of customers that enter a store during one day is an example of

a discrete random variable

Variance is

a measure of the dispersion of a random variable

Each individual outcome of an experiment is called

a sample point

A normal distribution with a mean of 0 and a standard deviation of 1 is called

a standard normal distribution

A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a

binomial probability distribution

In a standard normal distribution the value of z

can be any value

In an experiment, events A and B are mutually exclusive. If P(A) = 0.6, then the probability of B

cannot be larger than 0.4

A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the

classical method

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called

combination

A value of 0.5 that is added and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called

continuity correction factor

One of the basic requirements of probability is

if there are k experimental outcomes, then ∑P(Ei) = 1

If P(A) = 0.50, P(B) = 0.60, and P(A ∩ B) = 0.30, then events A and B are

independent events

The standard deviation of a standard normal distribution

is always equal to one

The probability that a continuous random variable takes any specific value

is equal to zero

In a standard normal distribution, the range of values of z is from

minus infinity to infinity

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

mutually exclusive

The variance is a measure of dispersion or variability of a random variable. It is a weighted average of the

squared deviations from the mean

If you are conducting an experiment where the probability of a success is 0.2 per day and you are interested in finding the probability of 4 successes in in three days, the correct probability function to use is

the Poisson probability function

The addition law is potentially helpful when we are interested in computing the probability of

the union of two events

For a normal distribution, a negative value of z indicates

the z is to the left of the mean

If P(A∪B) = 0.87 and P(A∩B) = 0.00, then P(B) = ?

there is not sufficient information to answer this question

The variance for the binomial probability distribution is

var(x) = nP(1 - P)

Given that Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754?

± 1.16

The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. Refer to Exhibit 5-7. The probability that Pete will catch fish on exactly one day is

.096

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?

1.08

Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?

1.54

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

1/2

A six-sided die is tossed 3 times. The probability of observing three ones in a row is

1/216

If a six sided die is tossed two times, the probability of obtaining two "4s" in a row is

1/36

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?

10

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What is the minimum weight of the middle 95% of the players?

151

The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.

2.4

Assume that you have a binomial experiment with p = 0.3 and a sample size of 100. The value of the variance is

21

If P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B)

None of these alternatives is correct.

If the mean of a normal distribution is negative,

None of these alternatives is correct.

If A and B are independent events, then

P(A) must be equal to P(A│B)