Question

Suppose that the commuting time on a particular train is uniformly distributed between 42 and 62 minutes. Bold a. What is the probability that the commuting time will be less than 49 ​minutes? Bold b. What is the probability that the commuting time will be between 45 and 55 ​minutes? Bold c. What is the probability that the commuting time will be greater than 58 ​minutes? Bold d. What are the mean and standard deviation of the commuting​ time?

Answer 1

For uniform distribution whole data is distribute equally.if we take x interval anywhere it's distribution ,the probability will be same.

For given problem data is distributed between 42 and 62.

We know

no of chances total chances Probability

Here total chance will be 62-42=20

A)

For commuting time less than 49,no of chances is 49-42=7

So probability is

7 Probability45) 20

B)

Between 45 and 55 ,no of chances is 55-45=10

10 0.5 Probability(45 55) = 20

C)

No of chances for greater than 58 is 62-58=4

Probability( 58) = 0.2 20 l

D)

For normal distribution in interval [a,b]

4262 ab Mean -52

62-425 77350269 5.77 b- a Standard deviation V12 V12