Suppose the shoe-size of students Stat 200 is normally distributed,with a mean o

Question

Suppose the shoe-size of students Stat 200 is normally distributed,with a mean of 10.0, and a standard deviation of 0.5. Aclueless shoe manufacturer is going to introduce a new line ofshoes specifically for Stat 200 students. How many pairs ofeach of the following sizes should be included in a batch of 1,000pair of shoes?

a)      8.5

b)      9.0

c)      9.5

d)     10.0

e)      10.5

f)       11.0

g)      11.5

P(X<8.5) * 1000
P(8.5<X<9.0) * 1000
P(9.0<X<9.5) * 1000
P(9.5<X<10.0) * 1000
P(10.0<X<10.5) * 1000
P(10.5<X<11.0) * 1000
P(11.0<X<11.5) * 1000

Explanation / Answer

The mean is 10, SD=0.5
FOr example, .3085 is in the table for the z score for 0.5, so30.85% of the folks are above 0.5 and 30.85% are below -0.5. DOnt forget that the normal distribution has a big bump in themiddle and two smaller tails on either side. If the tails have (30.85% x 2) then they have 61.7%, and thereare 100%-61.7=29.3% within the middle bump -0.5 to +0.5. Obviously half are below and half are above, so 29.3/2=14.65%are 9.5 to 10 and and 14.65% are 10 to 10.5.
If you dont understand that, just looking at a table orgetting the answer will not help you understand the concept, andyou are not likely to do well in your course. Please resist thetemptation to just get the answer - think about the concept.
Now, what if .3085 was a wrong value, what if you just want tolook up the answer and dont care, then go to a tablecalled area under the normal curve and get the answers (I hope youhave already stopped reading by now...)
0.5 .19 - so.. 190 shoes 1,0 .34 - so.. another 150 shoes (.34 -.19) 1.5 .43 - so.. 430 - (190+140) = 430-340= 90 shoes 2.0 .48 - 50 shoes 2.5 .49 - 10 shoes 3.0 .498 (almost a full 50%) - so

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