6. On a typical weekday morning customers arrive at a village post office independently and at a rate of 3 per 10 minute period.
Find the probability that
- at least 4 customers arrive in the next 10 minutes,
- no more than 7 customers arrive between 11.00 a.m. and 11.30 a.m.
The period from 11.00 a.m. to 11.30 a.m. next Tuesday morning will be divided into 6 periods of 5 minutes each.
- Find the probability that no customers arrive in at most one of these periods.
The post office is open for \(3 \frac { 1 } { 2 }\) hours on Wednesday mornings.
- Using a suitable approximation, estimate the probability that more than 49 customers arrive at the post office next Wednesday morning.
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