Question

If a normally distributed data set has a mean of81 and a standard deviation of 6, which of thefollowing represents approximately 95% of thedata?

Answer 1

Answer:

95% of the data is represented as 69 to 93 (option G)

Explanation:

Given:

mean of data = 81

standard deviation = 6

To find:

The option that represents 95% of the data

To determine the right option, we will apply the empirical rule (68-95-99.7%):

68% of the data will fall within 1 standard deviation

95% of the data will fall within 2 standard deviation

99.5% of the data will fall within 3 standard deviation

$\begin{gathered} 2\text{ standard deviation is represented as:} \\ \mu\text{ }\pm\text{ 2\sigma} \\ where\text{ \mu = mean, \sigma = standard deviation} \end{gathered}$

substitute the values:

$\begin{gathered} μ\pm2σ\text{ = 81 }\pm\text{ 2\lparen6\rparen} \\ =\text{ 81 }\pm\text{ 12} \\ 81\text{ }\pm\text{ 12 means 81 - 12 , 81 + 12} \\ =\text{ 69, 93} \\ This\text{ means 95\% of the data is represented from 69 to 93 \lparen option G\rparen} \end{gathered}$