The mean amount purchased by each customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. The population is positively skewed. For a sample of 50 customers, answer the following questions:
- What is the likelihood the sample mean is at least $25.00?
- What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
- Within what limits will 90% of the sample means occur?