MATH 1040 - Introduction to Statistics

Lesson 16.1 Practice Calculating Probabilities

On this page, we will be practicing using Normal Distributions. We will practice with the following question:

The average number of calories in a 1.5-ounce chocolate bar is $\mu=210$. Suppose that the distribution of calories is approximately normal with $\sigma=10$.

  1. Find the probability that a randomly selected chocolate bar will have less than 200 calories.
\[z = \frac{200 - 210}{10} = \frac{-10}{10} = -1\] \[P(z < -1) = 0.1587 = 15.87\%\]
  1. Find the probability that a randomly selected chocolate bar will have more than 225 calories.
\[z = \frac{225 - 210}{10} = \frac{15}{10} = 1.5\] \[P(z > 1.5) = 1 - P(z < 1.5) = 1 - 0.9332 = 0.0668 = 6.68\%\]
  1. Find the probability that a randomly selected chocolate bar will have between 200 and 220 calories.
\[z_a = \frac{200 - 210}{10} = \frac{-10}{10} = -1\] \[z_b = \frac{220 - 210}{10} = \frac{10}{10} = 1\] \[P(z < 1) = 0.8413 \qquad P(z < -1) = 0.1587\] \[P(-1 < z < 1) = P(z < 1) - P(z < -1) = 0.8413 - 0.1587 = 0.6826 = 68.26\%\]