Question

A particular fruit's weights are normally distributed, with a mean of 281 grams and a standard deviation of 33 grams. If you pick one fruit at random, what is the probability that it will weigh between 291 grams and 299 grams

Answer 1

0.0882

Explanation:

Given that:

Mean(m) = 281

Standard deviation (s) = 33

Probability of weight between 291 and 299 gram

Obtain the standardized score (Zscore):

P (X ≤ 291)

Zscore = (x - m) / s

Zscore = (291 - 281) / 33

Zscore = 10 / 33 = 0.303

P(Z ≤ 0.303) = 0.61906 (Z probability calculator)

P (X ≤ 299)

Zscore = (x - m) / s

Zscore = (299 - 281) / 33

Zscore = 18 / 33 = 0.5454

P(Z ≤ 0.5454) = 0.70726 (Z probability calculator)

Hence, probability of weight between 291 and 299 gram = 0.70726 - 0.61906 = 0.0882