Question

The time of a typical Fortnite match is normally distributed, with mean 20 minutes and standard deviation 10 minutes. We randomly sample 15 people. Include the Case or Rule you are in, and the calculator function.

a. What is the probability that the average match time is more than 23 minutes?

b. How long are the 5% longest average length of Fortnite matches?

Answer 1

mean = 20 and sd = 10
n = 15

a)
P(X > 23)
= P(z > (23 - 20)/(10/sqrt(15))
= P(z > 1.1619)
= 0.1226

b)
z-value for the longest length = 1.645

xbar = 20 + 1.645*10/sqrt(15)
xbar = 24.2474
i.e. 24.25 min