Use the 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values. A bell-shaped distribution with mean 1200 and standard deviation 15 .

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

Let X the random variable who represent the courtship time (minutes).

From the problem we have the mean and the standard deviation for the random variable X. [tex]E(X)=1200, Sd(X)=15[/tex]

So we can assume [tex]\mu=1200 , \sigma=15[/tex]

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

Solution to the problem

We can find the limits of the interval like this:

[tex] Lower = \mu -2*\sigma = 1200-2*15= 1170[/tex]

[tex] Upper = \mu +2*\sigma = 1200+2*15= 1230[/tex]

jainveenamrata jainveenamrata · Answer 2 · 2022-02-05T11:37:55+01:00

The interval will be from 1170 to 1230.

Statistics

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, summarise the data.

Given

The mean was 1200 and the standard deviation was 15.

To find

The interval.

How to get the interval?

The interval is given by mean ± 2x standard deviation.

For the upper limit

mean + 2 x standard deviation

1200 + 30

1230

For the lower limit

mean - 2 x standard deviation

1200 - 30

1170

Thus the interval will be from 1170 to 1230.

More about the statistics link is given below.

https://brainly.com/question/10951564