The average middle-distance runner at a local high school runs the mile in 4.5 minutes, with astandard deviation of 0.3 minute. What is the probability that a runner will run the mile in less than 4 minutes?

Question

Possible Answers:
A)7%B)3%C)5%D)4%

I know it's C, but I don't know how to get it.

Can someone please show me a step by step solution, please. I am completely lost.

Answer 1

4 min is .5 min below the mean ... 1.667 standard deviations

-1.667 is called the z-score

a z-score table will show the fraction of the population at or below this point

the table actually shows about 4.8%

Answer 2

Best normal distribution applet on line:
http://davidmlane.com/normal.html
enter:
mean : 4.5
SD : 0.5
click on below, enter 4 to get .047799..
or 4.8% as Scott stated.