Question

Date are drawn from a bell-shape distribution with a mean of 170 and a standard deviation of 5. There are 1700 observations in the data set. Approximately what percentage of the data are less than 180?

Answer 1

97.73%

Explanation:

Mean (μ) = 170

Standard deviation (σ) = 5

Assuming a normal distribution, for any observed value, X, the z-score is determined by:

`z=(X-\mu)/(\sigma)`

For X = 180:

`z=(180-170)/(5)\\ z=2`

A z-score of 2 corresponds to the 97.73-th percentile of a normal distribution.

Therefore, the percentage of data that is less than 180 is 97.73%.