6. A lock-keeper on canal has lots of free time on her hands, so she has undertaken some statistical analysis of boat arrivals at her lock. She has come to the conclusion that the number of boats arriving in a given time period has a Poisson distribution.

(a)The lock-keeper has data on the number of boats arriving for 360 consecutive onehour periods. During 27 of those one-hour periods, no boats arrived. Estimate the total number of boats that arrived in the 360 hours.

(b)What is the standard deviation in the number of boats arriving per day (24 hours)?

(c)About how many of the 360 one-hour periods had more than 1 boat arrive?

(d)What is the mean number of minutes between boat arrivals?