Example 6.6 from Statistics, 6.1 The Standard Normal Distribution

The Standard Normal Distribution: example 6.6

From 1984–1985, the mean height of 15-to 18-year-old males from Chile was 172.36 cm, and the standard deviation was 6.34 cm. Let Y = the height of 15-to 18-year-old males in 1984–1985. Then Y ~ N(172.36, 6.34).

About 68 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.
About 95 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________ respectively.
About 99.7 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. About 68 percent of the values lie between 166.02 cm and 178.7 cm. The z-scores are –1 and 1.
2. About 95 percent of the values lie between 159.68 cm and 185.04 cm. The z-scores are –2 and 2.
3. About 99.7 percent of the values lie between 153.34 cm and 191.38 cm. The z-scores are –3 and 3.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

The scores on a college entrance exam have an approximate normal distribution with mean, µ = 52 points and a standard deviation, σ = 11 points.

About 68 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.
About 95 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.
About 99.7 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

The scores on a college entrance exam have an approximate normal distribution with mean, µ = 52 points and a standard deviation, σ = 11 points.

About 68 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.
About 95 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.
About 99.7 percent of the y values lie between what two values? These values are ________________. The z-scores are ________________, respectively.

Solution

Your turn

Solution

Your turn