Question

The proportion of observations from a standard Normal distribution with values less than $1.15$ is

(a) $0.1251$.

(b) $0.8531$.

(c) $0.8749$.

(d) $0.8944$.

(e) none of these.

Short answer

The proportion of observations from a standard Normal distribution with values less than $1.15$ is$0.8749$.

Step-by-step solution

Given Information

$\mu =\text{Mean}=80$

$\sigma =\text{Standard deviation}=2$

$z=\mathrm{z}-\mathrm{score}<1.15$

Explanation

Use the appendix normal probability table to determine the corresponding probability.

The standard normal probability table in the appendix,$P(Z<1.15)$is found in the row that begins with $1.1$and in the column that starts with $0.05$

$P(Z<1.15)=0.8749$

Therefore, in a Standard Normal distribution, about $0.8749$ out of every $1,000$ observations has a value less than $1.15$.

Therefore, option (c) is the correct answer.