Ch. 6 LS - Econ 221

The accompanying table shows a portion of the z table. Find the probability that Z is greater than -2.22.

0.09868 P(Z>-2.22) = 1-P(Z<= -2.22) = 1 - 0.0132 = 0.9868

The area under a normal curve below its expected value is _____.

0.50

The probability that a normal random variable X is less than its mean is equal to

0.50

Since the z table provides the cumulative probabilities for a given value of z, how can we calculate P(Z>z)?

1-P(Z<=z)

The accompanying table shows a portion of the z table. Find the z value that satisfies P(Z>z) =0.0951

1.31

The accompanying table shows a portion of the z table. Find the z value that satisfies

1.41

The height of the probability density function f(x) of the uniform distribution defined on the interval [a,b] is

1/ (b-a) between a and b, and zero otherwise

An investment strategy has an expected return of 12 percent and a standard deviation of 10 percent. If investment returns are normally distributed, the probability of earning a return less than 2 percent is CLOSEST to:

16%

How many parameters are needed to fully describe any normal distribution?

2

An investment strategy has an expected return of 12 percent and a standard deviation of 10 percent. If investment returns are normally distributed, the probability of earning a return of more than 32 percent is CLOSEST to:

2.5%

For data that are normally distributed, the percentage of the data that falls within two standard deviations of the mean is

95.44%

Which of the following random variables is depicted with a bell-shaped curve?

A normal random variable

T/F: A discrete random variable can assume an uncountable number of values.

False: a discrete random variable assumes a countable number of values

It is known that the length of a certain product X is normally distributed with M=20 inches. How is the probability P(X>16) related to the probability P(X<16)?

P(X>16) is greater than P(X<16)

Due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to

P(Z<-1.5)

The probability that the normal random variable Z is less than 1.5 is equal to

P(Z>-1.5)

The z table provides the cumulative probabilities for a given z. What does 'cumulative probabilities' mean?

The probability that Z is less than or equal to a given z value

What does it mean when we say that the tails of the normal curve are asymptotic to the x-axis?

The tails get closer and closer to the x-axis but never touch it

Consider data that are normally distributed. In order to transform a value x into it standardized value z, we use the following formula:

Z = (x - M)/o

The probability that a discrete random variable X assumes a particular value x is

between zero and one.

For a continuous random variable X, the number of possible values

cannot be counted

For a continuous random variable X, the function used to find the area under f(x) up to any value x is called the

cumulative distribution function

For a continuous random variable, one characteristic of its probability density function f(x) is that the area under f(x) over all values of x is

equal to one

The probability distribution of a discrete random variable is called its probability _____.

mass function

The normal distribution is completely described by these two parameters:

mean and variance

The variance of the standard normal distribution is equal to _____.

one

The probability distribution of a continuous random variable is called its

probability density function

All of the following are examples of random variables that likely follow a normal distribution EXCEPT

the number of states in the USA, it is not a variable

A manager of a women's clothing store is projecting next month's sales. Her low-end estimate of sales is $25,000 and her high-end estimate is $50,000. She decides to treat all outcome for sales between these two values as equally likely. If we define the random variable X as sales, then X follows the

uniform distribution

Consider data that are normally distributed. In order to transform a standard normal value z into its under standardized value x, we use the following formula:

x = M + zo

The probability that a continuous random variable X assumes a particular value x is

zero.