Cars run a red light at a particular intersection at the rate of 3 cars per day.

Question

Cars run a red light at a particular intersection at the rate of 3 cars per day. Suppose we take a random sample of 40 days and count the number of cars that run the red light each day. Determine the sampling distribution of the sample mean. Mean: _______ Standard Error: _______ Shape: _______ Reason for Shape: _______ Suppose we want to calculate the probability that the sample mean number of cars that run the red light is less than 2.8 per day. If possible, calculate this probability. If not, briefly explain why it cannot be calculated.

Explanation / Answer

here as it is poisson distribution , hence mean number of cars for one day =3

and std deviation =(3)1/2=1.732

1) for 40 days , sample mean =3

std error =std deviation/(n)1/2 =1.732/(40)1/2 =0.274

shape : aprroximately normal

reason: as per central limit theorum, when sample size reaches to a considerable size, the distribution is approximately normal.

(ii) from normal distribution : zscore =(X-mean)/std deviation

P(X<2.8) =P(Z<(2.8-3)/0.274)=P(Z<-0.7303)=0.2326

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