# Normal Distribution, Probability Density Function, Frequency Distribution

Dear OTA,

Please explain with necessary steps.

Thanks

1. In its standardized form, the normal distribution:

A. has a meaning of 0 and a standard deviation of 1

B. has a mean of 1 and a variance of 0

C. has a total area equal to 0.5

D. is left-skewed

2. If a particular data set is approx. normally distributed, we would find that:

A. the mean would be approx. equal to the median

B. the range will be about 6 times the standard dev.

C. approx. 19 of every 20 observations would fall between +-2 standard deviations.

D. all of the above

3. For a uniform probability density function:

A. the height of the function cannot be less than 1

B. the height of the function is the same for each value of x

C. the height of the function is different for various values of x

D. the height of the function decreases as x increases

4. A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a (an):

A. normal probability distribution

B. uniform probability distribution

C. exponential probability distribution

D. Poisson probability distribution

5. The expected value of a discrete random variable is:

A. a weighted average over all possible outcomes

B. the sum of the possible outcomes

C. an adjusted median

D. equal to the median

6. Identify whether each is A. Discrete or B. Continuous

How many potholes there are in a 1-mile stretch of highway:

What is the time between arrivals at a tollbooth:

How many sheets of tissue paper in each box:

What is the diameter of the rods after the lathing process:

How much does a package weigh:

7. It is desirable that each class grouping or interval in a frequency distribution be:

A. of equal height

B. equal in width

C. coded with the same color

D. labeled by its lower bound

8. The descriptive measure of variation that is based on the concept of a deviation about the mean is:

A. the range

B. the interquartile range

C. the absolute value of the range

D. the standard deviation

9. Revising probabilities when new information is obtained requires the application of _______ _________. (It is a two-word answer and I didn't find answer in book, so whatever logical answer(s) you come up with will be fine.)

10. One of the major measures of quality of service provided by any organization is the speed with which the organization responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department has expanded from 2 installation crews to and installation supervisor, a measurer, and 15 installation crews. During a recent year, the company got 50 complaints concerning carpet installation. The following data (contained in the file furniture.xls) represent the number of days between the receipt of the complaint and the resolution of the complaint:

54 5 35 137 312 27 152 2 123 81 74 27 11 19 126 110 110 29 61 35 94 31 26 5 12 4 165 32 29 28 29 26 25 1 14 13 13 10 5 27 4 52 30 22 36 26 20 23 33 68

a) Construct a frequency distribution and a percentage distribution

b) Construct a histogram and percentage polygon

c) Form a cumulative percentage distribution and plot a cumulative percentage polygon

Do your calculations in an Excel file, please.

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#### Solution Summary

This solution provides answers to various statistics questions in Excel.

Probability distribution for discrete random variables

From past experience, an automobile insurance company knows that a given automobile will suffer a total loss with probability .02, a 50% loss with probability .08, or a 25% loss with probability .15 during a year. What annual premium should the company charge to insure a $10,000 automobile, if it wishes to "break even" on all policies of this type? (Assume there will be no other partial loss)

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