3.4/3.5 Normal Distribution

If X~N(10, 2²), then the standard deviation equals

Annual rainfall in Coastville is normally distributed with a mean of 60 cm and a standard deviation of 7 cm. For what percent of the years will the annual rainfall be between 53 cm and 60 cm?

For X~N (6, 2²) the z-score of x = 4.5 is

The z-score corresponding to the 44th percentile is

If X~N(35, 3²), what percent of the data are greater than 37? Round to the nearest percent.

If X~N(35, 3²), what percent of the data are between 30 and 37? Round to the nearest percent.

If X~N(35, 3²), what percent of the data are less than 29? Round to the nearest percent.

To earn a scholarship, Luc needs to score in the 87th percentile on an entrance test. If test marks are normally distributed with a mean of 400 and a standard deviation of 28, what mark (to the nearest whole number) is he aiming for?