Automated Teller Machine

Question

1)Arrivals to a an automated teller machine atm are distributed according to a Poisson distribution with a mean equal to three per 15 minutes.

a) Determine the probability that in a given 15 minutes segment no customers will arrive at the atm.

b) What is the probability that fewer than four customers will arrive in a 30 minute segment?

2)A population of 10 items contains 3 that are red and 7 that are green. What is the probability that in a random sample of 3 items without replacement, 2 red and 1 green items are selected?

Question

The management of the seaside golf club regularly monitors the golfers on its course for speed of play. Suppose a random sample of golfers was taken in 2005 and another random sample of golfers was selected in 2006. The results of the two samples are as follows: 2005 x bar 1=225 s1=20.25 n1=36 2006 xbar=219 s2=21.70 n2=31 based on the sample results, can the management of the seaside golf conclude that the average speed of play was different in 2006 that in 2005?

Conduct the appropriate hypothesis test at the 0.10 level of significance. Assume that the management of the club is willing to accept the assumption that the populations of playing times for each year are approximately normally distributed with equal variance.