The Average tnumber of customers coming at a university caf is 35 per hour. Customer arrivals occuur randomly

and independently of one another.

Each customer spends between a minimum of $4 and a maximum of $20 with each amount in between

being equally likely. On average throughout the day, 1 out of 6 customers have to order their second

Preference item(s), because the University cafe is out of stock of their first preference. The customer spend remains

the same regardless of whether they purchased their first or second preference

a)

What is the probability that out of these 40 customers who arrive in the next hour

[4 marks]

more than 80% of them receive their first preference item?

b)

If 45 customers arrive in the next hour, what is the probability that they spend more than

$10 on a average?

[6 marks]

c)

What is the probability that at least 32 customers will arrive in the next hour?

[ 4 marks]

d)

What is the standard deviation of the number of customers per hour?

[4 Marks]