The weights of apples of a certain variety are normally distributed with a mean of \(175\) grams and a standard deviation of \(15\) grams. Apples weighing less than \(150\) grams are classified as small.
(a) Find the probability that a randomly selected apple is classified as small. [3]
(b) In a batch of 500 apples, find the expected number of small apples. [2]
(c) The heaviest 5% of the apples are classified as extra large. Find the minimum weight for an apple to be classified as extra large. [2]
Question
Find the probability that a randomly selected apple is classified as small. [3]
Hint
Hint
Hint
Standardize using \(z = \frac{150 – 175}{15}\) and look up the probability in the normal table.
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\(P(W < 150) \approx 0.0478\)
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Question
In a batch of 500 apples, find the expected number of small apples. [2]
Hint
Hint
Hint
Multiply the probability found in part (a) by 500.
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Approximately 24 apples
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The heaviest 5% of the apples are classified as extra large. Find the minimum weight for an apple to be classified as extra large. [2]
Hint
Hint
Hint
Find \(k\) such that \(P(W \le k) = 0.95\) using the inverse normal function.
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Approximately 200 grams
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