Question

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 5 inches. What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall?

Answer 1

Answer: We can start by standardizing the values using the standard normal distribution:

z_1 = (65 - 66) / 5 = -0.2

z_2 = (67 - 66) / 5 = 0.2

Using a standard normal distribution table or calculator, we can find the area under the curve between -0.2 and 0.2:

P(-0.2 < Z < 0.2) = 0.0796

Therefore, the probability that an 18-year-old man selected at random is between 65 and 67 inches tall is approximately 0.0796 or 7.96%.

Step-by-step explanation: