SOLUTION: A children�s shoemaker knows that the shoe sizes of children under 10 are normally distributed with a mean of 5 and a standard deviation of 1.5. To guarantee that the middle 68% o

Question 1062363: A children�s shoemaker knows that the shoe sizes of children under 10 are normally distributed with a mean of 5 and a standard deviation of 1.5. To guarantee that the middle 68% of children can buy a pair of his shoes that are not too small, what sizes must be manufactured
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
68% is 1 sd on either side.
These are discrete data. There are no sizes 6.3, for example.
Sizes 5, 5.5,6,6.5,7,7.5,8
This would have mean 6.5.
For the next 2 sd s, then the sizes would have to be increased 3 on both ends.
The sizes needed are from 2 to 11. ANSWER
This has a mean of 6.5 with 3 sd s on either side.
The +/- 1 sd or 68% in the middle would encompass sizes 5 through 8.

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