While the histogram is not perfectly symmetric (there is mild right skewness), it is close enough to being symmetric and mound-shaped to justify. Suppose the distribution of calories in a Chipotle meal can be considered symmetric and mound-shaped with mean 1071 calories and standard deviation 301 calories. Answer the following questions.a. What is the approximate percentage of the Chipotle meals that have more than 469 calories?b. What is the approximate percentage of Chipotle meals with calorie amounts between 1372 calories and 1673 calories?c. If a particular meal's calorie amount is equal to the 16th percentile of Chipotle meal calorie amounts, how many calories are in the meal?

1) The 68-95-99.7 rule tells us how a distribution is divided. 99.7% of the distribution should fall within 3; 95%, 2 and 68%, 1 standard deviation from the mean.

As you can see in the graph.

a). What is the approximate percentage of the Chipotle meals that have more than 469 calories?

By the rule

We have the interval 68% is equal to the mean plus 1 standard deviation and minus one standard deviation.

So

[tex]68\%=(\mu-2\sigma,\mu+2\sigma)=(1071-2(301), 1071+2(301)=(469,1672)[/tex]

But the question wants to know more than 469 calories, then[tex]13.6\%+34\%+34\%+13.6\%+2.1\%=97.1\%\\[/tex]

b. What is the approximate percentage of Chipotle meals with calorie amounts between 1372 calories and 1673 calories?

Check the graph below

This percentage is the interval, which is a quarter of that 95%

[tex](\mu +\sigma,\mu+2\sigma)=(1372,1673)=\frac{95\%}{4}=13.6\%[/tex]

c.. If a particular meal's calorie amount is equal to the 16th percentile of Chipotle meal calorie amounts, how many calories are in the meal?

Since we're dealing with a Normal Curve, then to find the 16th percentile we need:

The Mean and Standard deviation
The Z score and then multiply by that Standard Deviation
Add this to the mean

.[tex]Z\: score=-0.994\\\\(-0.994)*301=-299.194\\-299.194+\mu \Rightarrow -299.194+1071=771.806\approx772[/tex]

We have the location 772 = 16th percentile. Since this meal is equal to 16th percentile, then this meal has 772 calories.