The length of time patients must wait to see a doctor at an emergency room in a

Question

The length of time patients must wait to see a doctor at an emergency room in a larger hospital has a uniform distribution between 40 minutes and 3 hours. What is the probability density function for this uniform distribution? What is the probability that a patient would have to wait between one and two hours? What is the probability that a patient would have to wait exactly one hour? What is the probability that a patient would have to wait no more than one hour? For a certain gas station the daily demand for gasoline is normally distributed with a mean of 500 gallons and a standard deviation of 75 gallons. Find the probability that the station will sell less than 665 gallons of gas on a given day. Find the probability that the station will sell between 482 and 527 gallons of gas.

Explanation / Answer

here uniform distribution parameter a=40 minutes and b=3*60=180 minutes

32)probabilty density function f(x) =1/(b-a) =1/140

33)P(60<X<120)=(120-60)/140=6/14

34)P(X=1) =0 ; as it is continuous fucntion for which point probabilty=0

35)P(X<60)=(60-40)140=2/14=1/7

36)P(X<665)=P(Z<(665-500)/75)=P(Z<2.2)=0.9861

37)P(482<X<527)=P((482-500)/75<Z<(527-500)/75)=P(-0.24<Z<0.36)=0.6406-0.4052=0.2354

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