stats decision chapter 7

What does it mean when we say a random variable is standardized?

A random variable x is standardized when each value of x has (the mean of x) subtracted from it, and the difference is divided by (the standard deviation of x.)

Which of the following are not correct concerning the probability distribution for any continuous random variable? a. The vertical coordinate is the probability density function. b. The range of the random variable is found on the y-axis. c. The total area represented under the curve will be equal to 1.00. d. The probability that x will take on a value between a and b will be the area under the curve between points a and b. e. The area under the curve represents the sum of probabilities for all possible outcomes.

B

In a continuous probability distribution, the probability that x will take on an exact value: a. is equal to the height of the curve at that value. b. is calculated using the probability density. c. is always equal to 0. d. is always greater than 0. e. None of these is correct.

C

What are continuous probability distributions?

Continuous probability distributions describe probabilities associated with random variables that are able to assume any of an infinite number of values along an interval

True or False: Any normal distribution is a symmetrical, bell-shaped curve, with mean = 0.0 and standard deviation = 1.0.

False

Explain what we mean by saying a random variable is approximately normally distributed

If the probabilities for the outcomes of the random variable are approximately equal to the areas under the normal curve, its distribution is approximately normal.

Explain why the total area beneath a probability density function is equal to 1.0.

The area beneath the probability density function represents the probability of the random variable, x, being between . Since x must be between (this is a certain event), the area must be equal to 1.0.

Why is the probability that a continuous random variable takes on any specific value equal to zero?

The probability that a continuous random variable takes on any specific value is equal to zero because there is an infinite number of possible values.

True or False: Continuous probability distributions describe probabilities associated with random variables that can take on any value along a given range or continuum and for which there are no gaps between these possible values.

True

True or False: For any specified interval of values, the probability that a continuous random variable x will assume a value within the interval is the area beneath the curve between the two points describing the interval.

True

True or False: In the normal distribution, the total area beneath the curve represents the probability for all possible outcomes for a given event

True

True or False: There exists a different normal curve for every possible pair of M and SD.

True

True or False: Under certain conditions, the normal distribution can be used to approximate the binomial distribution.

True