# The weights of the tomatoes is normally distributed. If the middle 83% weigh between 2.14 ounces...

## Question:

The weights of the tomatoes is normally distributed. If the middle {eq}83\% {/eq} weigh between {eq}2.14 {/eq} ounces and {eq}5.13 {/eq} ounces, then what is the mean weight of the tomatoes?

## Confidence Interval:

Confidence Interval gives two value based on test statistics in which population parameter lies with certain proportion of times

{eq}P(c_1 \leq \theta \leq c_2)=1-\alpha {/eq}

We are given that

83% confidence Interval for mean is 2.14 and 5.13 ounces

We need to find mean weight of tomatoes

Since we know that confidence Interval of normal distribution is always in the form of {eq}\mu-c \sigma \qquad \mu +c \sigma {/eq}

So mean is given as {eq}\frac{c1+c2}{2}=\frac{2.14+5.13}{2}=3.635 {/eq}