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
[tex]\begin{gathered} 2\text{ standard deviation is represented as:} \\ \mu\text{ }\pm\text{ 2\sigma} \\ where\text{ \mu = mean, \sigma = standard deviation} \end{gathered}[/tex]
substitute the values:
[tex]\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}[/tex]
