Question

timetto complete a quiz is distributed 7-14 minties (a) write a pdf and sketch it f(t)

what is the probability that a randimly selected student has no more than 9 mins between 10 to 14 find the mean time find the variance

Answer 1

I have answered the question below

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

Answer:

(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)

No more than 9 minutes

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

c)

Between 10 - 14 minutes

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

d)

Mean time is

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

e)

Variance is

variance σ 2 T = =  4.0833 minutes