Question

1. The area under the curve must add up to one for

   	a.	all density functions.
   	b.	just one density function.
   	c.	no density function.
   	d.	a special group of density functions.

3 points   

QUESTION 2

1. If the mean of a normal distribution is negative,

   	a.	the variance must also be negative.
   	b.	the standard deviation must also be negative.
   	c.	a mistake has been made in the computations, because the mean of a normal distribution can not be negative.
   	d.	Standard deviation can be any number but it must be positive.

3 points   

QUESTION 3

1. For a normal distribution, a negative value of Z indicates

   	a.	a mistake has been made in computations, because z is always positive.
   	b.	the area corresponding to the z is negative.
   	c.	the z is to the right of the mean.
   	d.	a value that is below the mean.

3 points   

QUESTION 4

1. The probability density function refers to:

   	a.	probability function for a discrete random variable.
   	b.	probability function for a continuous random variable.
   	c.	probability function for either a discrete or a continuous random variable.
   	d.	not enough information

Answer 1

1. To be a probability density function the necessary condition is that the area under the curve must add up to one.

a. All density functions

2. The mean of a normal distribution can be negative. But the variance can't be negative because it is always positive or zero. And standard deviation is square root of Variance. So atan deviation also can't be negative.

d. Standard deviation can be any number but it must be positive.

3. The formula to calculate z score for any observation X is

Mu is the mean and sigma is the stand deviation.

Then z is negative only when x is less than the mean.

d. A value that is below the mean.

4. Both the discrete and continuous random variable has probability density function but for discrete variables we often call them probability mass function. So if a probability density function is given it refers to a continuous random variable or a discrete random variable.

C. Probability function for either a discrete or a continuous random variable.