Statistics Chapter 7 Practice

In a large bag of candies, 20% are green and the rest are other colors. A handful of candies has 30 pieces. What is the probability that eight or more of them are green? Use the normal approximation of the binomial distribution.

.2467

One out of the four cars at a dealership is white. If they sell 20 cars at random, what is the probability that 6 or less will white? Use the normal approximation. Hint pi=1/4

0.78

On average a customer service call line handles a call every three minutes. Use the exponential distribution to find the probability that the next call will arrive in less than five minutes.

0.81

The duration of red lights in a city follows a uniform distribution from one to four minutes. What is the probability that you will wait at a randomly chosen red light between 2.5 to 3 minutes?

1/6

The time it takes a wholesaler to fill an order follows a uniform distribution from three to six days. What is the probability that they will fill an order between day 3 and 5?

2/3

A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 400 and 500?

21%

A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700?

27%

Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 560 and 490?

28%

Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 560 and 640?

31%

Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 550 and 650?

39%

A college entrance exam has scores that follow a normal distribution with a mean of 540 and standard deviation of 110. About 68% of students taking the exam will score within what range?

430 to 650

What do we mean when we say there is a "family" of normal distributions? Choose two of these statements.

A single equation describes all normal distribution. Distributions may have different means and standard deviations but still be "normal" in shape.

Choose the two statements below which accurately characterizes a Uniform Distribution.

Areas within the distribution represent probabilities The area inside the rectangle (i.e. the frequency polygon) must be one.

Why is it possible to use the Normal distribution (which is continuous) as a substitute for the Binomial distribution (which is discrete) for large sample sizes? Choose the best explanation.

As n increases, the difference between the probabilities for a Normal and a Binomial distribution become small.

Which of the following statements describe the purpose or characteristics of the z-value?

It has a mean of 0 and a standard deviation of 1. It is the distance from the mean, measured in units of the standard deviation. It converts any normal distribution to the standard normal distribution.

Where does the curve of the normal distribution touch the x-axis?

It never touches, but approaches asymptotically in both directions.

What are the upper and lower limits of the random variable for the Normal distribution?

No limits. It is asymptotic in both directions.

Which of the following is the best description of the shape of a Uniform Distribution?

Rectangular

Choose the statement that best characterizes the kind of events described by an Exponential distribution.

The events occur independently and at a constant rate per unit of time or length.

What determines the width and location of the Normal Distribution?

The mean (U) determines the location and standard deviation (o) determines the width.

What are the defining characteristics of the Standard Normal Distribution? Choose two.

The mean (U) is zero. The standard deviation (o) is 1.

Under what circumstances is the Normal distribution a good approximation to the Binomial distribution? Choose two answers.

The sample size times the probability of success is at least 5. The sample size times the probability of failure (1-P(success)) is at least 5.

What kind of events are described by an Exponential distribution?

Times between events in a sequence.

Choose the statement that describes the mean of a Uniform Distribution. a) It is smaller than the median and is skewed toward the minimum value of x. b) It is the middle class and is equal to the median. c) It can be calculated from the probability of success and the number of samples. d) It is greater than the median, and is skewed toward the maximum value of x.

b) It is the middle class and is equal to the median.

The average weight of an apple in a box is 110 grams and the standard deviation is 20 grams. What is the z-value for an apple that weights 140 grams? a) z=-1.5 b) z=1.5 c) z=2.5 d) z=30

b) z=1.5

The normal distribution has a ________ shape with a mean of u and a standard deviation of o.

bell

An I.Q. test has scores that follow a normal distribution with a mean of 105 and standard deviation of 10. About 95% of persons taking the test will score within what range? a) 75 to 105 b) 95 to 115 c) 85 to 125 d) 105 to 125

c) 85 to 125

Which of the following best describes the conditions necessary for the Normal approximation to the Binomial distribution?

npi and n(1-pi) are both at least 5.

The Normal Distribution is ________ about the mean.

symmetrical

The average height for an American male is 71 inches and the standard deviation is 3 inches. What is the z-value for a height of 68 inches?

z=-1

The average score of an IQ test is 110 and the standard deviation is 10 grams. What is the z-value for a score of 130?

z=2