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kozerog [31]
3 years ago
8

In a normally distributed data set with a mean of 24 and a standard deviation of 4.2, what percentage of the data would be betwe

en 15.6 and 32.4 and why?
Mathematics
1 answer:
valentinak56 [21]3 years ago
8 0

Answer:

About 95% of data lies between 15.6 and 32.4

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 2.4

Standard Deviation, σ = 4.2

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Empirical Formula:

  • Almost all the data lies within three standard deviation from the mean for a normally distributed data.
  • About 68% of data lies within one standard deviation from the mean.
  • About 95% of data lies within two standard deviations of the mean.
  • About 99.7% of data lies within three standard deviation of the mean.

We have to find the percentage of data lying between 15.6 and 32.4

15.6 = 24 - 2(4.2) = \mu - 2\sigma\\32.4 = 24 + 2(4.2) = \mu + 2\sigma

Thus, we have to find the percentage of data lying within two standard deviations of the mean. By Empirical formula about 95% of data lies between 15.6 and 32.4

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