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 55 people. How many would you expect to be between 170 and 175 cm?
A) 34
B) 19
C) 17
D) 25
E) 23

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 55 people. How many would you expect to be between 170 and 175 cm? 
A) 34 
B) 19 
C) 17 
D) 25 
E) 23

Quizplus · Accepted Answer

To find the number of people between 170 and 175 cm, we need to calculate the area under the normal curve between these two values. Using a standard normal distribution table or calculator, we can find that the area between 0 and 1 standard deviations above the mean (i.e., between 170 and 175 cm) is approximately 0.1977.

To convert this to the actual number of people, we need to multiply by the total number of people, which is 55:

0.1977 x 55 = 10.87

Rounding to the nearest whole number, we get:

Answer: B) 19

Therefore, we can expect about 19 people out of 55 to have heights between 170 and 175 cm.

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