Mathematics: 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?

they are 13 units apartStep-by-step explanation:...

Suppose that the commuting time on a particular train

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21.01.2022

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 commutingtime?

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

2)SD =

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

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