The mean amount bought by typical customer at Churchill's Grocery Store is $23.50 with standard deviation of $5.00. Suppose the distribution of amounts purchased follows normal distribution. For the sample of 50 customers, answer the following problems.
1. What is the likelihood the sample mean is at least $25.00?
2. What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
3. Within what limits will 90 percent of the sample means occur?