The number of transactions made per hour in a small store is under investigation
ID: 3228327 • Letter: T
Question
The number of transactions made per hour in a small store is under investigation. The number of transactions per hour can be well modeled using a Poisson distribution with rate . The sales manager in the store recorded the number of transactions in seven independent day long periods; the store is open for ten hours per day. The number of transactions were: 72, 68, 40, 100, 90, 85, 75. (a) Estimate the rate . Hence, or otherwise, estimate the probability of no transactions in an hour long time period. (b) Determine a 90% upper confidence limit for the mean number of transactions per day. Hence, find a 90% lower confidence limit for the probability of no transactions in an hour long time period. Carefully state any distributional results that you use in your derivation.
Explanation / Answer
Given nos 72, 68, 40, 100, 90, 85, 75
Mean = 75.714
Probability that no transactions per day
= p(x=0)
= e^(-T) T^x/ x!
= 0
B) standard deviation of above nos = 19.27
Ci = x +/- t * s/ sqrt (n)
= 75.714 +/- 3.707* 19.27/sqrt (7)
T value from t table at degree of freedom 6
Limits arw
48.714 to 102.713