He 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.

10.56% of apples  are with diameters less than 3.5 inches.  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4 inches

Standard Deviation, σ = 0.4 inches

We are given that the distribution of apple size is a bell shaped distribution that is a normal distribution.

Formula:

a) P(apples with diameter less than 3.5 inches)

P(x < 3.5)

Calculation the value from standard normal z table, we have,  

10.56% of the apples will fall through a screen with mesh size of 3.5 inches that 10.56% of apples  are with diameters less than 3.5 inches.

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