The diameters of apples from a certain farm follow the normal distribution with mean 4 inches...
The diameters of apples from a certain farm follow the normal distribution with mean 4 inches and standard deviation 0.4 inch. Apples can be size-sorted by being made to roll over mesh screens. First the apples are rolled over a screen with mesh size 3.5 inches. This separates out all the apples with diameters less than 3.5 inches. Second, the remaining apples are rolled over a screen with mesh size 4.3 inches. Find the proportion of apples with diameters less than 3.5 inches.
- Round your answer to four decimal places.
Homework Answers
Solution:
Given: The diameters of apples from a certain farm follow the normal distribution with mean 4 inches and standard deviation 0.4 inch.
Thus X ~ Normal 
We have to find: the proportion of apples with diameters less than 3.5 inches.
P( X < 3.5 )= ...............?
Find z score for x = 3.5
Thus we get:
P( X < 3.5 )= P( Z < -1.25 )
Look in z table for z = -1.2 and 0.05 and find corresponding area.
P( Z < -1.25 )= 0.1056
thus
P( X < 3.5 )= P( Z < -1.25 )
P( X < 3.5 )= 0.1056
Thus the proportion of apples with diameters less than 3.5 inches is 0.1056
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