Respuesta :
Answer:
99.7% data lies between 13 to 43
Step-by-step explanation:
Mean: [tex]\mu = 28[/tex]
Standard deviation : [tex]\sigma = 5[/tex]
68% of data lies between [tex]\mu - \sigma[/tex] to [tex]\mu +\sigma[/tex]
95% of the data lies between [tex]\mu - 2\sigma[/tex] to [tex]\mu +2\sigma[/tex]
99.7% data lies between [tex]\mu - 3\sigma[/tex] to [tex]\mu +3\sigma[/tex]
We are supposed to find 99.7 of the data will lie between which values
99.7% data lies between [tex]28 - 3(5)[/tex] to [tex]28 +3(5)[/tex]
99.7% data lies between 13 to 43
Hence 99.7% data lies between 13 to 43
You can use the empirical rule for normal distribution to get the value needed.
According to the Empirical Rule, 99.7 of the data with specified property will lie between 13 and 43
What is empirical rule?
According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
Symbolically for 99.7%, we have:
[tex]P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%[/tex]
where we have [tex]X \sim N(\mu, \sigma)[/tex] (X is normally distributed with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])
Using the above fact to find the range of 99.7% data with specified property
Since the mean for given data is [tex]\mu =28[/tex] and standard deviation is [tex]\sigma = 5[/tex],
thus, according to empirical rule, 99.7% of the data will lie in range
[tex][ \mu - 3\sigma, \mu + 3\sigma][/tex] = [tex][ 28 - 15, 28 + 15] = [13, 43][/tex]
Thus,
According to the Empirical Rule, 99.7 of the data with specified property will lie between 13 and 43
Learn more about empirical rule here:
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