You are a marketing manager for a very important shopping center in your city. You are interested in studying the behavior of buyers with respect to the amount spent and the time they make their purchases in order to propose a new advertising campaign that also involves granting certain discounts and promotions.

It has been concluded from the study that 70% of the shoppers in the shopping center make their purchases on weekends and also spend more money during that period.

If the amount of money buyers spend on Saturdays between 5 pm and 8 pm has a normal distribution with mean $ 90 and standard deviation of $ 5. Then you select a buyer at random and want to determine how they will spend their money.

 1. What is the probability that he spent more than $ 90? And the one that has spent less than USD 90?

2. What is the probability that he spent between $ 80 and $ 100?

3. Standardize the probability distribution

4. Find the probability that you spent less than $ 50 but using the new standardized function.

5. Represent graphically.