Question

A particular fruit's weights are normally distributed, with a mean of 686 grams and a standard deviation of 24 grams.

The heaviest 18% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

solution:

Given data

Mean () = 686

Standard deviation () = 24

Let X be the normal random variable representing weights of fruits

Let X1 be the weight of fruits such that P(X>=X1) = 0.18

P(X<X1) = 1-0.18

   = 0.82

= 0.82

= 0.9155 [using standard normal distribution table ]

X1 - 686 = 21.972

X1 = 707.972

Therefore, The heaviest 18% of fruits weigh more than 707.972 grams

P(X>707.972) = 18% = 0.18