Loyalty programs are a great promotional idea for retail stores to show their appreciation of repeat customers. A certain retail store wants to adopt a new platform for its loyalty program. Instead of blanket promotions, they classify customers depending on what amount they spend and approach them with personalized offers. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this retail store will be normally distributed with a mean of $84 and a standard deviation of $30.

(a) If the management's assumptions are correct, what percent of customers will spend $49 or less?

Using your calculations, round the z -value to 2 decimal places and enter the z -value here:

Express the final answer in percentage, round to 2 decimal places (for example, 0.0735 should be converted to 7.35%),

and enter here: %

(b) What percent of customers will spend between $49 and $100?

Express the final answer in percentage, round to 2 decimal places (for example, 0.0735 should be converted to 7.35%),

and enter here: %

(c) The management wants to give extra points of loyalty program to 4% of the customers who spend most. What would be the amount which separates top 4% of the distribution from the bottom 96%?

Using your solution, enter the z -value in 2 decimal places here:

Round the final answer to 2 decimal places and enter here: