Question

A peach farmer has two different varieties (named Variety A and Variety B) of peach trees on her land. Twenty percent of her trees are Variety A peaches and the other 80% are Variety B peaches. The weights of Variety A peaches are normally distributed with a mean of 92 grams and a standard deviation of 8 grams. The weights of Variety B peaches are normally distributed with a mean of 103 grams and a standard deviation of 13 grams.

What weight of a Variety B peach corresponds to the third quartile of the distribution?

Answer 1

We have the districution for B given as

mean = 103 gms

and sd=13gms

now we are looking for 3rd quartile of the distribution and hence the z score for 75% area under the curve from the z table is

z=0.6744898

Hence

z= (Xbar-mu)/sd

0.6744898 = (Xbar-103)/13

So., Xbar=111.7684

So the third quartile of the distribution for for the weight of a Variety B peach has weight of 111.7684

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