Characteristics of Normal Distribution

In the standard normal distribution, the value of standard deviation is?

1

What are the eight characteristics of a normal distribution?

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

To use the normal approximation for the binomial distribution, np and nq must be equal to at least what value?

10

Approximately 95% of scores in a normal distribution fall within?

2 standard deviations of the mean.

A normal distribution has a mean equal to 5. What is the value of the median and mode in this distribution?

5

A probability distribution for binomial outcomes approximates the shape of what type of distribution?

A normal distribution

Identify the column in the unit normal table for each of the following: A. z-scores are listed in which column? B. the area from z-scores toward the tail is listed in which column? C. The are between a z-score and the mean is listed in which column?

A. Column A B. Column C C. Column B

All of the following characteristics are true about a normal distribution expect: a. The mean can be any positive or negative number. B. The variance can be any positive number. C. The shape of the normal distribution is symmetrical. D. The tails of a normal distribution​ touch the x-axis at the 3 SD from the mean.

D. Tails of a normal distribution touch the x-axis at the 3SD from the mean

In the standard normal distribution, the values of the mean is ?

O

The area under a normal curve ranges from 0 to 1 and can never be negative. What type of statistics also has these same characteristics?

Probability

What term best describes behavior that falls within 2SD of the mean in a normal distribution?

Statistical Norms

State two step for locating scores in a distribution with a given probability?

Step 1: locate the z-score associated with a given proportion in the unit normal table. Step 2: transform the z-score into a raw score

State the two steps for locating proportion under the normal curve?

Step 1: transforms a raw score (X) into a z-score Step 2: locate the corresponding probability for the z-score in the unit normal table

True or False: The larger is the sample size, the more closely a binomial probability distribution will approximate a normal distribution?

True

What does the binomial distribution approximates to the normal distribution imply?

When the same size is large, the binomial distribution more closely approximates to the normal distribution.

The normal distribution is used to determine the probability of a certain outcome _____________ to all other outcomes.

in relation or relative

5% of scores fall ?

outside 2SD of the mean

What is a normal distribution?

theoretical distribution which includes the data that are symmetrically distributed around the mean as well as the median and the mode.

What is a Z-score?

value of a standard normal distribution. Or the numerical values of a z-socre identifies the distance of a value from its mean.