The average sales are $$15,000$ and the standard deviation is $500.$ Assuming sales follow a normal distribution, what is the probability that sales will be greater than $17,000?($Show your work. You must first calculate the $Z$ score $(3$ POINTS$).$ Then calculate the answer $(4$ POINTS$).$

The following is sales data by month:

$15$ Jan

$20$ Feb

$27$ March

$21$ April

$30$ May

$35$ June

$30$ July

$35$ August

$27$ September

$22$ October

$24$ November

$18$ December

a$)(2$ POINTS$)$ Using a moving average with three periods, determine the demand for next January. $($Show how you figured it out$)$

b$)(2$ POINTS$)$ Using a weighted moving average with three periods, determine the demand for January. Use $4,2,1$ for the weights of the most recent, second most recent, and third most recent. For example, if you were forecasting for January $-$ October would have a weight of $1,$ November would have a weight of $2,$ and December would have a weight of $4.$

c$)(2$ POINTS$)$ What is the MAD for the $3$ month moving average?

d$)(2$ POINTS$)$ What is the MAD for the weighted moving average?

e$)(1$ POINT$)$ Which is better based upon MAD?