Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 36 seconds. What is the proportion of men having running times faster than 120 seconds?

a ...34

b ...227

c ...773

d. None of the answer options is correct.

Answer: b ...227

Step-by-step explanation:

Since the running times for 400 meters are Normally distributed for young men between 18 and 30 years of age, we would apply the the formula for normal distribution which is expressed as

z = (x - u) / s

Where

x = running times

u = mean time

s = standard deviation

From the information given,

u = 93 seconds

s = 36 seconds

We want to find the proportion of men having running times faster than 120 second. It is expressed as

P (x > 120) = 1 - P (x ≤ 120)

For x = 120,

z = (120 - 93) / 36 = 0.75

Looking at the normal distribution table, the probability corresponding to the z score is 0.7734

P (x > 120) = 1 - 0.7734 = 0.227