Question

A particular fruit's weights are normally distributed, with a mean of 323 grams and a standard deviation of 30 grams.If you pick one fruit at random, what is the probability that it will weigh between 220 grams and 307 gramsRound to 3 decimal places.

Answer 1

The mean weight is 323 g, and the standard deviation is 30 g.

Then the Z-score for 220 g is (220 - 323)/30 = -3.43, and the Z-score for 307 g is (307 - 323)/30 = -0.53.

Then, according to the normal table, the probability of finding a fruit at random with weight between 220 and 307 is given by:

P(220 < x < 307) = P(Z < -0.53) - P(Z < -3.43) = 0.2981 - 0.0003 = 0.2978

Answer: 0.298