The weights of apples produced by an orchard are normally distributed with a mean of 160 grams and a standard deviation of 15 grams.
(a) Find the probability that an apple chosen at random weighs more than 175 grams. [2]
(b) Find the probability that an apple chosen at random weighs between 150 grams and 180 grams. [2]
(c) 5% of the apples are classified as ‘extra large’. Find the minimum weight for an apple to be classified as ‘extra large’. [3]
Question
Find the probability that an apple chosen at random weighs more than 175 grams. [2]
Hint
Hint
Hint
Calculate the z-score: \(z = (175-160)/15\) and then use \(1-\text{normalCdf}\) for that value.
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\(P(W>175) \approx 0.159\)
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Question
Find the probability that an apple chosen at random weighs between 150 grams and 180 grams. [2]
Hint
Hint
Hint
Convert 150 and 180 to their respective z-scores and use the normalCdf for the interval.
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\(P(150 < W < 180) \approx 0.656\)
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Question
5% of the apples are classified as ‘extra large’. Find the minimum weight for an apple to be classified as ‘extra large’. [3]
Hint
Hint
Hint
Find the 95th percentile using the inverse normal function: \(invNorm(0.95, 160, 15)\).
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Minimum weight ≈ 185 grams
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