Suppose the neck size of men is normally distributed, with a mean of 15.5 inches and a standard deviation of 0.5 inch. A shirt manufacturer is going to introduce a new line ofshirts. Assume that if your neck size falls between two shirt sizes, you purchase the next larger shirt size. How many of each of the following sizes should be included in a batchof 1,500 shirts? (Assume that if your neck size falls below 14 you will purchase a size 14 shirt. Assume that if your neck size falls above 17 you will not purchase a shirt. Note:The answer blanks may not add up to exactly 1,500 shirts. Round your answers to the nearest whole number.)(a)14shirt(s)(b)14.5shirt(s)(c)15X shirt(s)(d)15.5x shirt(s)(e)16shirt(s)(f)16.5shirt(s)(g)17shirt(s)

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Step 1

Hey, since there are multiple subpart questions posted, we will answer first three subpart questions. If you want any specific subpart question to be answered then please submit that subpart question only or specify the subpart question number in your message.”

Step 2

Solution:

a.

The number of shirts is obtained below:

The population mean is 15.5 inches and standard deviation is 0.5 inches. The total number of shirts in a batch is 1,500.

From the Excel,

“=NORM.DIST(14,15.5,0.5,TRUE)]” in EXCEL software.

The probability -value is 0.0013.

The required value=1,500x0.0013= 2.0248.

The number of shirts is 2.0248.

Step 3

b.

The number of shirts is obtained below:

From the Excel,

“=NORM.DIST(14.5,15.5,0.5,TRUE)]” in EXCEL software.

The probability -value is 0.0228.

The required value=1,500x0.0228= 34.125.

The number of shirts is 34.125.

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