While the histogram is not perfectly symmetric (there is mild right skewness), it is close enough to being symmetric and mound-shaped to justify using the 68-95-99.7 rule. Suppose the distribution of calories in a Chipotle meal can be considered symmetric and mound-shaped with mean 1060 calories and standard deviation 291 calories.

Required:

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?

Answer:

97.9% ; 12.4% ; 771

Step-by-step explanation:

The approximate percentage who have more Than 469 calories :

P(x > 469)

Mean, m = 1060

Standard deviation, s = 291

Z = (x – mean) / standard deviation

Z = (469 – 1060) / 291

Z = −2.030927

P(Z > – 2.031) = 1 – P(Z < – 2.031)

P(Z > – 2.031) = 1 – 0.0211

P(Z > – 2.031) = 0.9788 = 97.9%

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

[(1673 – 1060) / 291] – [(1372 – 1060) / 291]

P(Z <2.106) – P(Z < 1.072)

0.9824 – 0.85814

= 0.12426 = 12.4%

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

The Zscore at 16 percentile = -0.994

Zscore = (score – mean) / standard deviation

-0.994 * 291 = score – 1060

−289.254 = score – 1060

Score = −289.254 + 1060

Score = 770.746

Approximately 771