Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. What is the probability that a person selected at random is taller than 175 cm? Please, round your answer to three decimal places, if necessary.
A) 0.841
B) 0.159
C) 0.5
D) 0.977
E) 0.842

Question

Quizplus · Accepted Answer

We need to find the probability that a person selected at random is taller than 175 cm. Since heights are normally distributed with a mean of 170 cm and a standard deviation of 5 cm, we can use the standard normal distribution formula to standardize the value of 175 cm into a standard normal variable, as follows:

Z = (x - μ) / σ
Z = (175 - 170) / 5
Z = 1

Then, we can find the area to the right of this value in a standard normal distribution table or calculator, which represents the probability of being taller than 175 cm. The area to the right of Z = 1 is approximately 0.159, which means that the probability of selecting a person at random with a height taller than 175 cm is about 0.159 or 15.9%.
Therefore, the best choice is B.

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