B.5. Let assume that the probability distribution of the duration of a flight fr

Question

B.5. Let assume that the probability distribution of the duration of a flight from Kansas City, MO to Miami, FL can be approximated by a uniform distribution presented below: 10 270 sx s 280 0 elsewhere f(x) = (a) What is the probability that the duration of the flight will at least 274 min, that is, P(x £ 274) (b) Calculate the average duration of a flight between these two cities (c) Calculate the standard deviation of the duration (d) Please indicate the time for (d.1) an early flight and (d.2)a late flight based on your answers from (b) and (c)

Explanation / Answer

Ans:

it is uniform distribution:

a=270,b=280

f(x)=1/(280-270)=1/10

Cumulative distribution function:

F(x)=P(X<=x)=(x-270)/(280-270)=(x-270)/10

a)P(at least 274 min)=P(x>=274)=1-(274-270)/10=1-(4/10)=1-0.4=0.6

P(atmost 274 min)=P(x<=274)=(274-270)/10=4/10=0.4

b)Avearge=(a+b)/2=(270+280)/2=550/2=275

c)Variance=(b-a)2/12=(280-270)2/12=100/12=8.33

standard deviation=sqrt(8.33)=2.89

d)Early flight will have time less than 275 and late flight will have time more than 275 min. within 2.89 standard deviation of the mean.

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