Chapter 6 Probability, Normal Distributions, and z Scores

1. the normal distribution is mathematically defined. 2. the normal distribution is theoretical. 3. the mean, median, mode, are all located at the 50th percentile. 4. the normal distribution is symmetrical. 5. the mean can equal any value. 6. the standard deviation can equal any positive value. 7. the total area under the curve of a normal distribution is equal to 1.0. 8. the tails of a normal distribution are asymptotic.

Characteristics of the Normal distribution

can be any positive number it has a mean of 0 and variance of 1

The Standard Normal Distribution

True

The mean, median, and mode are all located at the 50th percentile in a perfect normal distribution.

85.56

a professor records the following final exam scores: 78+-7(M+-SD). Students scoring in the top 14% get an A. What is the cutoff score for the top 14% in this example?

-1.0

a researcher determines that students study an average of 80+-20(M+-SD) min/week. Assuming these data are normally distributed, what is the z score for students studying 60min/week?

1. fall above the mean 2. fall below the median 3. fall above and below the mode

in a normal distribtion, 50% of all data:

approximate

most behavior is believed to _______ a normal distribution.

standard normal transformation

the ________ converts any normal distribution with any mean and any variance to a standard normal distribution with a mean of 0 and variance of 1.

there are an infinite number of possible distributions

the mean can take on any value and the standard deviation can take on any positive value. Therefor,_____

that extreme score are possible in a normal distribution

what is the implication for the tails of a normal distribution being asymptotic?

-1.28

what is the z score for scores in the bottom 10%?

1.96

what is the z score for scores in the top 2.5%?

a normal distribution

what type of distribution does the binomial distribution approximate?

.5

which of the following is a possible value for the standard deviation of a normal distribution?

1. Find the real limits 2. check for normality 3. find the proportion located within the real limits

which of the following is an appropriate step for the normal approximation of the binomial distribution?

the proportion of area between z=+1 & z=-1

which proportion is largest in a z distribution?