Question

1. There is a lower limit but no upper limit for a random variable that follows the

	a.	​uniform probability distribution.
	b.	​exponential probability distribution.
	c.	​normal probability distribution.
	d.	​binomial probability distribution.

2. 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?

	a.	196
	b.	190
	c.	151
	d.	249

3. A scatter diagram reveals a strong positive linear relationship between oil and gasoline prices. Which of the following numerical techniques will not give us more detailed information about this relationship?

	a.	Coefficient of determination
	b.	Coefficient of correlation
	c.	Coefficient of variation.
	d.	All of these choices help us describe this relationship.

4. Which of the following statements is true for the following observations: 9, 8, 7, 9, 6, 11, and 13?

	a.	Only the mean and median are equal.
	b.	Only the mean and mode are equal
	c.	The mean, median, and mode are all equal.
	d.	Only the median and mode are equal.

Answer 1

1) For Uniform distribution, lower limit = a and upper limit = b

    For exponential distribution, lower limit = 0 and upper limit = infinity (no upper limit)

    For normal distribution, lower limit = -infinity and upper limit = +infinity

    For binomial distribution, lower limit = 0 and upper limit = n             (n is any natural number)

Correct answer is Exponential distribution

2) Here

Middle area = 0.95

Left area = (1 - 0.95)/2 = 0.025

Right area = (1- 0.95)/2 = 0.025

Z for left area = 0.025 is -1.96                 (From statistical table)

     = 200 + (-1.96) * 25

    = 200 - 49

    = 151

The minimum weight of middle 95% of the players is 151

3) Coefficient of variation

4) Observations in increasing order are as:

6 , 7 , 8 , 9 , 9 , 11 , 13

Mean = sum of all observations / total number of observations

          = 63 / 7

          = 9

Median = (n+1)/2 th observation

             = (7+1)/2 th observation

             = 4 th observation from increasing order sequence

            = 9

The mean, median and mode are all equal.