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

Step-by-step 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 :-

$f(x)=\dfrac{1}{b-a}\\\\=\dfrac{1}{52-42}=\dfrac{1}{10}, 42<x<52$

Thus, the required probability :-

$P(X<44)=\int^{44}_{42}f(x)\ dx\\\\=\int^{44}_{42}\dfrac{1}{10}\ dx\\\\=\dfrac{1}{10}[x]^{44}_{42}=\dfrac{1}{10}(44-42)=\dfrac{1}{5}=0.2$

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