Men's Shirt Sizes Are Determined By Their Neck Sizes. Suppose That Men's Sizes Are Approximately Normally Distributed With Mean 15.7 Inches And Standard Deviation 0.7 Inch. A Retailer Sells Men's Shirts In Sizes S, M, L, XL, Where The Sizes Are Defined In The Table Below. Because The Retailer Only Stocks The Sizes Listed Above, What Proportion Of Customers

 

3. Men's shirt sizes are determined by their neck sizes. Suppose that men's neck sizes are approximately normally distributed with mean 15.7 inches and standard deviation 0.7 inch. A retailer sells men's shirts in Sizes S, M, L, XL, where the shirt sizes are defined in the table below. Shirt size Neck size S 14 neck size 15 M 15 < neck size < 16 L 16 < neck size 17 XL 17 neck size 18 (a) Because the retailer only stocks the sizes listed above, what proportion of customers will find that the retailer does not carry any shirts in their sizes? Show your work (b) Using a sketch of a normal curve, illustrate the proportion of men whose shirt size is M. Calculate this proportion. (c) Of 12 randomly selected customers, what is the probability that exactly 4 will request size M Show your work