The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of...

The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 £ and a variance of 900 £2.

1. 
   

   1)  If the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?

   
   


2. 
   

   2)  In a sample of 100 customers, what are the number of customers whose expenditure is between 420 £ and 485 £?

   
   


3. 
   

   3)  What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 £?

   
   


4. 
   

   4)  In a sample of 49 customers, what are the number of customers whose mean expenditure is at least 410 £?

   
   


5. 
   

   5)  What is the probability that the expenditure of the first customer exceeds the expenditure of the second customer by at least 20 £?