Question

Time T to complete a quiz in class is uniformly distributed from 7 minutes to 14 minutes. (a) Write the pdf and sketch it f(t) =

Graph of pdf f(t) What is the probability that a randomly selected student takes (b) no more than 9 minutes? (c) between 10 to 14 minutes? (d) Find the mean time µT = (e) Find the variance σ 2 T =

Answer 1

(a)

T ~ Uniform(a = 7, b = 14)

The PDF of T is,

f(t) = 1/(14-7) = 1/7 for 7 t 14

= 0 otherwise,

Graph of pdf f(t) is,

(b)

P(T 9) = (9 - 7) / (14 - 7) = 2/7

(c)

P(10 T 14) = (14 - 10) / (14 - 7) = 4/7

(d)

µT = (a + b)/2 = (7 + 14)/2 = 10.5 minuts

(e)

variance σ 2 T = =  4.0833 minutes