Answer :
84.3 % is the required percent as per 68-95-99.7 rule.
The empirical rule is a statistical rule (also called the three-sigma rule or the 68-95-99.7 rule) which states that, for normally distributed data, almost all of the data will fall within three standard deviations either side of the mean.
- 68% of data within 1 standard deviation
- 95% of data within 2 standard deviations
- 99.7% of data within 3 standard deviations
Here, we have to solve according to 68-95-99.7 rule.
Standard deviation is a measure of spread; it tells how much the data varies from the average, i.e., how diverse the dataset is. The smaller value, the more narrow the range of data is.
Normal distribution is a distribution that is symmetric about the mean, with data near the mean are more frequent in occurrence than data far from the mean.
Let's proceed to solve the given question.
Given that, μ = 112 and σ = 20
68% of data falls within 1 standard deviations from the mean - between μ-σ and μ+σ.
95% of data falls within 2 standard deviations from the mean - between μ-2σ and μ+2σ.
99.7% of data falls within 3 standard deviations from the mean - between μ-3σ and μ+3σ.
Now, we just have to add the value of mean and standard deviation, we get
μ-σ = 112-20 = 92
μ+σ = 112+20 = 132
μ-2σ = 112-2x20 = 72
μ-2σ = 112+2x20 = 152
μ-3σ = 112-3x20 = 52
μ+3σ = 112+3x20 = 172
P(x < 132) = P(x-μ/σ < 132-112/20)
= P(x-μ/σ < 1)
= P(z < 1)
= 0.843
= 84.3 %
Therefore, 84.3 % is the required answer.
Learn more in depth about empirical formula at https://brainly.com/question/10093236
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