Question

The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65 minutes. Suppose the actual commuting time is uniformly distributed between 64 and 74 minutes.

What is the probability that the commuting time will be less than 70 minutes? (round to two decimal places) Answer

What is the probability that the commuting time will be between 65 and 70 minutes? (round to two decimal places) Answer

What is the probability that the commuting time will be greater than 65 minutes? (round to two decimal places)

Answer 1

Solution:-

a) The probability that the commuting time will be less than 70 minutes is 0.60.

a = 64, b = 74

x = 70

$P(x< 70)= 1- P(x\geq 70)$

$P(x<70)= 1- \frac{74-70}{74-64}$

$P(x<70)=1-0.40$

$P(x<70)=0.60$

b) The probability that the commuting time will be between 65 and 70 minutes is 0.50.

a = 64, b = 74

x₁ = 65,

x₂ = 70

$P(a,c,d,b) = \frac{d-c}{b-a}$

$P(65\leq x\leq 70) = \frac{70-65}{74-64}$

$P(65\leq x\leq 70) = 0.50$

c) The probability that the commuting time will be greater than 65 minutes is 0.90.

a = 64, b = 74

x = 65

$P(x,a,b)= \frac{b-x}{b-a}$

$P(x\geq 65)= \frac{74-65}{74-64}$

$P(x\geq 65)= 0.90$