23. The creators of a video game, Mortal Kombat, designed the game so that the amount of time necessary for a player to achieve basic proficiency (that is, understand the rules and advance to a higher level of play) has a Normal distribution with a mean of 2.5 hours and a standard deviation of 0.5 hours. Answer parts A-E below based on this information.

A. (4 points) The middle 95% of players should achieve basic proficiency between what two times?

B. (4 points) What is the probability that a randomly selected player requires less than 2.5 hours to become proficient?

C. (4 points) How long will it take for the fastest 20% of players to become proficient?

a. R: > qnorm(0.20, 2.5, 0.5) = 2.08 hours

b. R: > qnorm(0.80, 2.5, 0.5) = 2.92 hours

c. R: > qnorm(0.20, 0, 1) = -0.84 hours

d. R: > qnorm(0.80, 0, 1) = 0.84 hours

D. (4 points) What is the probability that a random player will take longer than 3 hours to become proficient?

a. R: > pnorm(1.00, 0, 1) = 0.8413

b. R: >1 pnorm(1.00, 0, 1) = 0.1587

c. R: > pnorm(1.00, 2.5, 0.5) = 0.0013

d. R: > 1 pnorm(1.00, 2.5, 0.5) = 0.9987

E. (4 points) Write out the R command you would use to find the probability that a player becomes proficient in less than 1 hour. For this problem you must use a Z-value.