Question

Suppose that the commuting time on a particular train is uniformly distributed between 40 and 50 minutes. Bold a. What is the probability that the commuting time will be less than 43 ​minutes? Bold b. What is the probability that the commuting time will be between 42 and 48 ​minutes? Bold c. What is the probability that the commuting time will be greater than 48 ​minutes? Bold d. What are the mean and standard deviation of the commuting​ time?

Answer 1

Answer:

a. 0.30

b. 0.60

c. 0.20

d. Mean = 45,  Standard Deviation = 2.8867

Step-by-step explanation:

a = 40, b = 50

a. What is the probability that the commuting time will be less than 43 ​minutes? Bold

P(X<43) = (43-40)/(50-40) = 0.30

b. What is the probability that the commuting time will be between 42 and 48 ​minutes? Bold

P(42<X<48) = (48-42)/(50-40) = 0.60

c. What is the probability that the commuting time will be greater than 48 ​minutes? Bold

P(X>48) = (50-48)/(50-40) = 0.20

d. What are the mean and standard deviation of the commuting​time?

1) Mean = (b+a)/2 = (40+50)/2= 45

2)SD =

$Standard Dev = \sqrt{(b-a)^2/12}\\Standard Dev = \sqrt{(50-40)^2/12} \\Standard Dev = \sqrt{100/12} \\Standard Dev= 2.8867$