Q:

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.

Accepted Solution

A:
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 inchesStandard Deviation, σ = 0.4 inchesWe 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.