Question

Chocolate Bar Calories The average number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normal with σ = 10. Find the probability that a randomly selected chocolate bar will have

a. Between 200 and 220 calories

b. Less than 200 calories

Source: The Doctor’s Pocket Calorie, Fat, and Carbohydrate Counter.

Answer 1

Let, X is the number of calories in a randomly selected chocolate bar

Given that X follows normal distribution with and

a)

We need to find the probability that on a randomly selected chocolate bar will have between 200 and 220 calories.

The z value corresponding to 200 is

The z value corresponding to 220 is

The area between z = 0 and z = – 2.50 is 0.4938.

The area between z = 0 and z = – 0.50 is 0.1915

Hence, the desired area is 0.4938 – 0.1915 = 0.3023, or 30.23%

That is,

Therefore, the probability that on a randomly selected chocolate bar will have between 200 and 220 calories is 0.3023

b)

We need to find the probability that on a randomly selected chocolate bar will have less than 200 calories.

The z value corresponding to 200 is

From the symmetric property of the normal distribution, the area to the left of – 2.50 is same as the area to the right of z = + 2.50

First find the area between 0 and + 2.50 and subtract it from 0.5000

The area between z = 0 and z = 2.50 is 0.4938, and the area to the right of

z = 2.50 is 0.0062, or 0.62%, obtained by subtracting 0.4938 from 0.5000

That is,

Therefore, the probability that on a randomly selected chocolate bar will have less than 200 calories is 0.0062