Question

The weight of oranges are normally distributed with a mean weight of 150 grams and a standard deviation of 10 grams. in a sample of 100 oranges, how many will weigh between 130 and 170 grams?

Answer 1

Given that mea = 150 and standard deviation = 10

sample size is n =100

standard deviation for the sample = sd/sqrt(n) = 10/sqrt(100) = 10/10 = 1

we have to find P(130<X<170)

using the formula

P(130<X<170) = P((x-mean)/s<z<(y-mean)/s)

= P((130-150)/1<z<(170-150)/1)

= P(-20<z<20)

= 1.0 (because 99.7% of data fall withiin 3 standard deviation and we are finding the probability of data falling between -20 to 20 standard deviation)

This means that for a sample of 100 oranges, 100% of the oranges wil weigh between 130 and 170 grams