Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 100 people. How many would you expect to be taller than 160 cm? Please, round your answer to the nearest integer.
A) 230 people
B) 98 people
C) 48 people
D) 16 people
E) 5 people

Question

Quizplus · Accepted Answer

We need to find the proportion of people taller than 160 cm and then multiply it by the total number of people (100) to get the expected number of people taller than 160 cm. To find the proportion, we can use the z-score formula:

z = (x - μ) / σ

where x is the height cutoff (160 cm), μ is the mean height (170 cm), and σ is the standard deviation (5 cm).

z = (160 - 170) / 5 = -2

Using a standard normal table or calculator, we find that the proportion of people taller than 160 cm is approximately 0.9772.

Expected number of people taller than 160 cm = proportion * total number of people
= 0.9772 * 100
= 97.72

Rounding to the nearest integer, we get 98 people. Therefore, the best choice is B.

Suppose That People's Heights (In Centimeters) Are Normally Distributed, with a Mean