Stat question 8

Question

A particular fruit's weights are normally distributed, with a mean of 284 grams and a standard deviation of 32 grams.

The heaviest 13% of fruits weigh more than how many grams?

Answer 1

Answer:

13% = 0.13

This means, 0.87 to the left of cumulative z-curve.

Hence, if we look at standard normal probabilities table, we see that when z= 1.127 (approx), area under the standard normal curve to the left 0.87. That is 0.13 to the right, that is 13%.

Now, we solve for x = mean + 1.127 * standard deviation

mean = 284 grams

standard deviation is 32 grams

Or, x = 284 + 1.127 * 32 = 284 + 36.064

Or, x = 320.064

Hence, heaviest 13% of fruits shall weigh more than 320.064 grams