Ten customers are waiting in line to pay for purchases at a busy retailer during the holidays. Let  denote the amounts bought by these customers, and model them as iid random variables with mean $150...

Ten customers are waiting in line to pay for purchases at a busy retailer during the holidays. Let
 denote the amounts bought by these customers, and model them as iid random variables with mean $150 and standard deviation $50.

a. What are the mean and standard deviation of the total amount purchased by these 10 customers?
⁸

b. Why is the standard deviation of the sum of the 10 purchases so much less than 10 times the standard deviation of each?⁹