Task 4: Coffee shop scheduling (9 marks total) The Lakeside Coffee Shop morning

Question

Task 4: Coffee shop scheduling

(9 marks total)

The Lakeside Coffee Shop morning customer load follows a normal distribution. The mean number of customers is 60 and the standard deviation is 15.

Determine the probability that the number of customers tomorrow will be 50. (3 marks)

If the store gets more than 70 customers, they need to have a fourth staff member working. What is the probability that they will need that fourth person tomorrow? (3 marks)

If the number of customers falls below 42, then two staff members are sufficient. What are the chances only two workers are required tomorrow? (3 marks)

Explanation / Answer

solution=

1.Determine the probability that the number of customers tomorrow will be 50.

This is a normal distribution

Z=(x-µ)/

=(50-60)/15

=-0.67

From table P(Z<-0.67)

=0.25249

2.If the store gets more than 70 customers, they need to have a fourth staff member working. What is the probability that they will need that fourth person tomorrow?

Z= Z=(x-µ)/

=(70-60)/15

=0.67

P(Z>0.67)=

1-P(Z<0.67

=1-0.74751

=0.25249

3.If the number of customers falls below 42, then two staff members are sufficient. What are the chances only two workers are required tomorrow?

This is the probability that there are 40

Z= Z=(x-µ)/

=(40-60)/15

=-1.3333

P(Z<-1.3333)=0.09121

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