Suppose that 32% of the apples grown on a particular orchard have blemishes that make it...

Suppose that 32% of the apples grown on a particular orchard have blemishes that make it difficult for them to be sold at a market. If a market purchases a crate that contains 100 apples selected randomly from the orchard, answer each of the following.
1. Find the mean and standard deviation for the number of blemished apples in the crate.
2. Compute the probability of there being exactly 32 blemished apples in the crate.
3. Would it be considered unusual for 40 or more of the apples to be blemished?

Expert Solution

Given n = 100 and p = 0.32

i) Using Binomial distribution,

Mean = np = 100*0.32 = 32

Standard Deviation= npq = 100*0.32*0.68 = 21.76

ii) The probability of there being exactly 32 blemished apples in the crate is

iii) Usual Interval: (Mean - 2SD, Mean + 2SD) = (32 - 2*21.76, 32 + 2*21.76) = (-11.52,75.52)

No, the observation 40 is unusal since it is in the above interval.

orchestra answered 1 year ago

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