Question

For scores that are normally distributed with a mean score of 120 and a standard

deviation of 20.

1) What % of the data is between 80 and 160?

2) What % of the data is below 100?

3) 68% of the scores are between what scores?

4) Find the z-score for a score of 155.

5) Find the z-score for a score of 90.

6) Find a score that is 3 standard deviations above the mean.

7) Find a score that is 2.5 standard deviations below the mean

Answer 1

Explanation:

The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. The calculation is as follows:

x = μ + (z)(σ) = 5 + (3)(2) = 11

The z-score is three.

The mean for the standard normal distribution is zero, and the standard deviation is one. The transformation

z=x-u/o produces the distribution Z ~ N(0, 1). The value x comes from a normal distribution with mean μ and standard deviation σ.