Question
goal their 20th shot ? Neptive on Dror 5. Cars arrive at a tollbooth at an average of 80 cars per hour. What is the probability that between 38 and 40 cars (inclusive) will arrive at the tollbooth in the next 30-minute time interval? Assume that the number of cars that arrive during non-overlapping time intervals are length h is proportional to h, and that the probability that two or more cars arrive in a sufficiently short time interval is essentially zero. 0aiss0 A salesperson can meet with either one or two customers each day, with probability 1/3 and 2/3, respectively. Each meeting will result in no sale or a $50,000 sale, with probability 0.9 and 0.1 respectively. When the salesperson meets with two customers in a day, the occurrence of a sale at one meeting is independent of the occurrence of a sale at the other meeting. 6. Let X represent the salesperson's daily sales Give the probability distribution for daily sales Find the mean and standard deviation for daily sales Find the moment generating function for daily sales. .
Explanation / Answer
5. 80 cars per hour = 80/60 cars in a minute
that means 40 cars in 30 minutes.
X=number of car passing in an interval of time
X follows poisson distribution with mean = 40 cars per 30 minutes.
P [ X=38 ] = 4038 exp-40 / 38! = 0.06137
P [ X=39 ] = 4039 exp-40 / 39! = 0.06295
P [ X=40 ] = 4040 exp-40 / 40! = 0.06295
P [ X=38] + P [X=39] + P[ x=40 ] = 0.06137+ 0.06295+ 0.06295 =
for a small time interval h,
rate is (80/60)*h cars / unit time = 4h/3
P[X=1] = (4h/3)1exp-(4h/3) / 1! = (4h/3) exp-(4h/3)
which is proportional to h.
0.18727
