Question

Suppose that the commuting time on a particular train is uniformly distributed between 42 and 52 minutes. Bold a. What is the probability that the commuting time will be less than 44 ​minutes

Answer 1

Answer: 0.2

Explanation:

Given: The commuting time on a particular train is uniformly distributed over the interval (42,52).

∴ The probability density function of X will be :-

`f(x)=(1)/(b-a)\\\\=(1)/(52-42)=(1)/(10), 42<x<52`

Thus, the required probability :-

`P(X<44)=\int^(44)_(42)f(x)\ dx\\\\=\int^(44)_(42)(1)/(10)\ dx\\\\=(1)/(10)[x]^(44)_(42)=(1)/(10)(44-42)=(1)/(5)=0.2`

Hence, the probability that the commuting time will be less than 44 ​minutes= 0.2