The weights of apples harvested from an orchard are normally distributed with a mean of 150 grams and a standard deviation of 15 grams.
(a) Find the probability that a randomly selected apple weighs more than 170 grams. [2]
(b) Find the probability that a randomly selected apple weighs between 140 grams and 165 grams. [3]
(c) 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 weighs more than 170 grams. [2]
Hint
Hint
Hint
Convert 170 grams to a z-score using \(z = (170 – 150)/15\) and use the normal cumulative distribution function to find the upper tail probability.
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Question
Find the probability that a randomly selected apple weighs between 140 grams and 165 grams. [3]
Hint
Hint
Hint
Calculate the z-scores for 140 and 165 grams, then use the cumulative normal probabilities to find the difference.
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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’. [2]
Hint
Hint
Hint
Use the inverse normal function with a cumulative probability of 0.95 (since 5% are above this weight) to find the cutoff.
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Complete Answer
175 grams
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