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 60 people. How many would you expect to be taller than 175 cm?
A) 8
B) 6
C) 4
D) 10
E) 20

Question

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 60 people. How many would you expect to be taller than 175 cm? 
A) 8 
B) 6 
C) 4 
D) 10 
E) 20

Quizplus · Accepted Answer

First, we need to standardize the cutoff value of 175 cm using the formula:
z = (x - μ) / σ
z = (175 - 170) / 5
z = 1
Then, using a standard normal distribution table or calculator, we can find the proportion of people taller than 175 cm:
P(z > 1) = 0.1587
Finally, we can calculate the expected number of people taller than 175 cm:
Expected value = Proportion * Total number of people
Expected value = 0.1587 * 60
Expected value ≈ 9.522
Rounding to the nearest whole number, we get 10, so the answer is D: 10.

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