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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.

Respuesta :

Answer:

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:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

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

P(x < 3.5)

[tex]P( x < 3.5) = P( z < \displaystyle\frac{3.5 - 4}{0.4}) = P(z < -1.25)[/tex]

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

[tex]P(x < 3.5) = 0.1056 = 10.56\%[/tex]

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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