Question

A particular fruit's weights are normally distributed, with a mean of 539 grams and a standard deviation of 25 grams.

If you pick one fruit at random, what is the probability that it will weigh between 496 grams and 621 grams

Answer 1

Let X denote the weights of a particular fruit

= 539 (mean)

= 25 (standard deviation)

Here we need to find the probability that X lies between 496 grams and 621 grams

which is same as:

As X follows normal so, will follow standard normal distribution

we denote

Here Z is standard normal variable

We get the values of P(Z<3.28) and P(Z<-1.72) from z table

Answer:The probability that it will weight between 496 grams and 621 grams is 0.9568