Question

Sam often runs 5Ks for time. His times are approximately normally distributed with a mean time of 26 minutes and a standard deviation of 2.3 minutes. Using the normalcdf function on your graphing calculator find the probability that Sam’s time is greater than 30 minutes (express your answer as a decimal rounded to three places).

Answer 1

= 26

= 2.3

To find P(X > 30):

Z =(30 - 26)/2.3

= 1.7391

Using the normalcdf function on graphing calculator :

Function: normalcdf (Lower boundary, Upper boundary, Mean, Standard Deviation)

In this problem, since we have to find P(X > 30):

Lower boundary = 30

Upper boundary = 1E99 for positive infinity

Mean = 26

Standard Deviation = 2.3

Substituting:

Function: normalcdf ( 30, 1E99, 26, 2.3)

we get:

P(X > 30):= 0.041

So,

Answer is:

0.041