Question

Heights (in inches) obtained by a group of people in a random survey are reported in the following table:

Height Probability
55 0.011
60 0.023
65 0.133
70 0.333
75 0.333
80 0.133
85 0.023
90 0.011
What is the expected height (in inches)?

Answer 1

The expected height is calculated by summing the product of each height with its probability, which yields an expected height of approximately 71.96 inches.

Step-by-step explanation:

To calculate the expected height in inches, which is a form of mathematical expectation in statistics, we will use the provided probabilities and heights. The expected height is given by the sum of each height times its corresponding probability.

1. Multiply each height by its probability:
   55 * 0.011 + 60 * 0.023 + 65 * 0.133 + 70 * 0.333 + 75 * 0.333 + 80 * 0.133 + 85 * 0.023 + 90 * 0.011.
2. Add these products together to find the expected value.
3. The calculation yields:
   55 * 0.011 + 60 * 0.023 + 65 * 0.133 + 70 * 0.333 + 75 * 0.333 + 80 * 0.133 + 85 * 0.023 + 90 * 0.011 = expected height.

To perform this calculation, let's sum up the values:
(55 * 0.011) + (60 * 0.023) + (65 * 0.133) + (70 * 0.333) + (75 * 0.333) + (80 * 0.133) + (85 * 0.023) + (90 * 0.011) = 71.96 inches (rounded to two decimal places).

Therefore, the expected height of a person from this group is approximately 71.96 inches.