The owner of the Coffee Bean Cafe states that she sells 500 cupcakes per day. Along with staple flavours, such as double chocolate and vanilla bean, which are always available, each day of the week has its own special—such as lemon—which is only baked on Tuesday. Therefore, cupcake sales are fairly consistent from day to day, and the number sold follows a normal probability distribution, with a standard deviation of 20 cupcakes. A random sample is taken over 36 days.
a. What is the standard error of the mean?
b. What is the probability that the average number of cupcakes sold is between 490 and 510 cupcakes?
c. What is the probability that the average number of cupcakes sold is more than 490 cupcakes?