Question

A particular fruit's weights are normally distributed, with a mean of 738 grams and a standard deviation of 14 grams. The heaviest 2% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Answer 1

Answer:

We get that the heaviest of fruits weigh 766.84 grams.

Step-by-step explanation:

We know that a particular fruit's weights are normally distributed, with a mean of 738 grams and a standard deviation of 14 grams.

We have:

$\mu=738\\\\\sigma=14$

We calculate x:

$P(X<x)=1-0.02\\\\P\left(\frac{X-\mu}{\sigma}<\frac{x-\mu}{\sigma}\right)=0.98\\\\P\left(\frac{X-738}{14}<\frac{x-738}{14}\right)=0.98\\\\P\left(Z<\frac{x-738}{14}\right)=0.98$

We use the standard normal table and we get: Z=2.06.

So, we get

$2.06=\frac{x-738}{14}\\\\x-738=28.84\\\\x=766.84$

We get that the heaviest of fruits weigh 766.84 grams.