Question

read, understand and analyze each question. choose the letter of the correct answer.

1. in a normal distribution, what percent of values lie below the mean?

a. 13.5%
b. 34%
c. 50%
d. 68%

1. in a normal distribution, what percent of values lie within two standard deviations?

a. 13.5%
b. 68%
c. 95%
d. 99.7%

1. in a normal distribution, what percent of value lie above 3 standard deviations?

a. 0.15%
b. 2.35%
c. 2.5%
d. 16%

Explanation:

1.

Step1: Recall normal distribution property

A normal distribution is symmetric about the mean.

Step2: Determine percentage below mean

Half of the data lies below the mean. Since half is \(50\%\), the answer is \(C\).

2.

Step1: Recall empirical rule

The empirical rule (68 - 95 - 99.7 rule) for normal distributions.

Step2: Find percentage within two standard deviations

According to the rule, about \(95\%\) of the data lies within \(2\) standard deviations of the mean. So the answer is \(C\).

3.

Step1: Use empirical rule and symmetry

The total percentage of data within \(3\) standard deviations is \(99.7\%\). The remaining percentage is \(100 - 99.7=0.3\%\). Due to symmetry, the percentage above \(3\) standard deviations is \(\frac{0.3}{2}=0.15\%\). So the answer is \(A\).

Answer:

1. C. \(50\%\)
2. C. \(95\%\)
3. A. \(0.15\%\)