Respuesta :
Answer: There is 95% of the data that will lie between 14 and 30.
Step-by-step explanation:
Since we have given that
Mean = 22
Standard deviation = 4
As we have the range between 14 and 30
1) First, we consider, 14, Then,
[tex]Mean-14\\\\=22-14\\\\=8[/tex]
which can be written as [tex]8=2(4)=2(Standard\ deviation)[/tex]
Thus, 70 is 2 standard deviations to the left of the mean.
Similarly,
2) If we consider 30,Then,
[tex]30-Mean\\\\=30-22\\\\=8[/tex]
which can be written as [tex]8=2(4)=2(Standard\ deviation)[/tex]
Thus, 30 is 2 standard deviations to the right of the mean.
According to Empirical Rule,
It is stated that within two standard deviation of the mean , there is about 95% of the data.
Hence, there is 95% of the data that will lie between 14 and 30.
You can use the empirical rule for the normal distributions (also called bell shaped distributions) to find the needed percentage.
The percent of the data that will lie between 14 and 30 in given distribution is 95%
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.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
where we had [tex]X \sim N(\mu, \sigma)[/tex]
where mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex]
How to find the percent of data lying in given range for specified bell shaped distribution?
Let the variable be X whose distribution is given.
Then, according to the data, we have [tex]X \sim N(22, 4)[/tex]
It can be seen that 14 is 22 - double of 4
and 30 is 22 + double of 4.
Thus, using the second statement of empirical rule stated above, we get:
[tex]P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\\\P(22 - 2 \times 4 < X < 22 - 2 \times 4) = 95\%\\P(14 < X < 30) = 95\%[/tex]
Thus,
The percent of the data that will lie between 14 and 30 in given distribution is 95%
Learn more about empirical rule here:
https://brainly.com/question/13676793
