Stat question 7

Question

A particular fruit's weights are normally distributed, with a mean of 287 grams and a standard deviation of 17 grams.

If you pick one fruit at random, what is the probability that it will weigh between 236 grams and 267 grams

Answer 1

A particular fruit's weights are normally distributed, with a mean of 287 grams and a standard deviation of 17 grams. If you pick one fruit at random, what is the probability that it will weigh between 236 grams and 267 grams

Mean = 287 grams

Standard Deviation = 17 grams

Calculate Z-scores:

Z(236) = (236 - 287)/17 = -3.0000

Z(267) - (267-287)/17 = -1.1765

If we look at the Z-table: Area under under standard normal curve:

For Z = -3.0000, Area under the standard normal curve on the left = 0.0013

For Z = -1.1765, Area under the standard normal curve on the left = 0.0388 (approx)

To obtain the desired probability in question, we have to get the difference between the two values:

If we pick one fruit at random:

The probability that it will weigh between 236 grams and 267 grams = 0.0388 - 0.0013 = 0.0375

The answer is: 0.0375 or, 3.75%