I'm stuck on a past paper question for S2:
A garden centre sells canes of nominal lenght 150cm, the canes are cought from a supplier who uses a machine to cut canes of length L where L ~ N(mu, 0.3^2)
a. find the value of mu, to the nearest .1 cm, such that there is only a 5% chance that a cane supplied to the garden centre will have length less than 150 cm.
I got the answer as 149.8
Where I'm stuck is b and c:
A customer buys 10
b. find the probability that at most 2 of the canes have length less than 150cm.
Do I stick with the normal distribution, or do I have to change to the binomial?
Another customer buys 500:
c. USing a suitable approximation, find the probability that fewer than 35 of the canes will have length less than 150cm.
Do I use binomial?
When can you expect yours?