Data Exam 4

Given that Z is a standard normal variable, the value z for which P(Z ≤ z) = 0.2580 is:

-0.65

The standard normal distribution has a mean and a standard deviation respectively equal to:

0 and 1

The sum of independent normally distributed random variables is normally distributed with mean equal to the sum of the individual means and variance equal to the sum of the individual variances. If X is the sum of two independent normally distributed random variables with respective means 100 and 200 and respective standard deviations 15 and 25, the probability that X is between 280 and 315 is closest to which of the following?

0.450

Given that Z is a standard normal random variable, P(-1.0≤Z≤1.5) is:

0.7745

If we plot a continuous probability distribution f(x), the total probability under the curve is:

1

Assume that round widgets from a manufacturing process have diameters that are normally distributed with mean 175.25 centimeters and standard deviation 2.35 centimeters. The chances that a randomly selected widget has diameter less than 166 centimeters is closest to which of the following?

1 out of 25,000

According to the empirical rule, how many observations lie within +/- 1 standard deviation from the mean?

68%

In a suburb of Los Angeles, 44% of the homes have an electronic security system. If three homes in this suburb are chosen at random, let P(all) be the probability that all of them have an electronic security system, and let P(none) be the probability that none of them have an electronic security system. Then P(all) and P(none) are which of the following (to the nearest three decimals)?

P(all) = 0.085, P(none) = 0.176

The higher the value of the density function f(x), _____.

The more likely the value x

Which equation shows the process of standardizing?

Z = (X - μ)/σ

A continuous probability distribution is characterized by:

a continuum of possible values

The mean μ of a probability distribution is a measure of:

central location

The normal distribution is a:

continuous distribution with two paremeters

One reason for standardizing random variables is to measure variables with:

different means and deviations on a single scale

The standard deviation σ of a probability distribution is a measure of:

the variability of the distribution

If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

to the right of the mean

The total area under the normal distribution curve is equal to one.

true