# Z-scores and random continuous variables

### Z-scores and random continuous variables

#### Lessons

• Introduction
a)

b)

• 1.
Translating Normal Distribution to Standard Normal Distribution
The heights of a population of women are normally distributed. The mean height is 164 cm with a standard deviation of 8 cm. What is the probability of a randomly selected woman who is shorter than 169 cm in this population?

• 2.
The age at which a group of children first started talking is normally distributed. The data set has a mean of 18 months and a standard deviation of 2.3 months. What is the percentage of this group of children who first started talking between 15 and 24 months?

• 3.
Finding Raw Data from Z-Scores
An environmental group did a survey on how much water a population consumed when taking shower and bath. It was found that the amount of water consumption is normally distributed with a mean value of 65 liters and a standard deviation of 4.3 liters. What is the amount of water that separates the least 90% from the most 10%?

• 4.
A school wanted to find out the physical fitness of its students. All students were asked to run for 400 meters on the track as fast as they could, and their finishing times were recorded. The distribution of the finishing times is normal. The mean finishing time is 75 seconds and the standard deviation is 5.5 seconds. What is the finishing time that represents the slowest 85% of students?