Normal Probability Distribution

Using Normal Distribution for Probability

Find the following proportions of the following:Find the following proportions of the following:

(1) z < .85(2) z > .85(3) z > 2.66(4) −.1 < z < .1

Warm-upWarm-up

= .8023= .1977= .0039= .0796

Normal Distribution as Probability Distribution

Example Problem 1Supposed there are a sample survey of 400 undergraduates students who have been asked if

they are going to report cheating between 2 people in a quiz . The study showed that 12%

would answer YES.

What is the probability that the survey result differs from the truth about the population by

more than 2 percentage point?p = 0.12

Ṕ = 0.12N (0.12, 0.016)

N(mean, sd) Ṕ=0.10 Ṕ=0.12 Ṕ=0.14

Ṕ=0.10 Ṕ=0.12 Ṕ=0.14

What is the probability that the survey result differs from the truth about the population by more than 2 percentage point?

P(0.10 ≤ Ṕ ≤ 0.14)= P (Z-score 1 ≤ Ṕ ≤ Z-

score 2)= P (-1.25 ≤ z ≤

1.25)= 0.8944 -

0.1056=

0.7888

= 1- 0.7888= .2112

Therefore, about 21% of sample results will be off by more than 2

percentage point