# Thread: normal distribution, find standard deviation

1. ## normal distribution, find standard deviation

a farmer supplies tomatoes to a grocery, with an average weight of 74 grams
weight of tomatoes is normally distributed about their mean
grocery has policy of rejecting tomatoes that weigh less than 70 grams
11% of the farmer's tomatoes have been rejected
what is the standard deviation?

i know z=(x-mean)/stdev, x=70, mean=74, P(X<70)=0.11 but i'm totally mind-blanking on how to find z and also stdev.
i think P(x<70)=P(Z<z), is that right?
any help is very much appreciated!
many thanks!!

2. Originally Posted by lalalamaths

a farmer supplies tomatoes to a grocery, with an average weight of 74 grams
weight of tomatoes is normally distributed about their mean
grocery has policy of rejecting tomatoes that weigh less than 70 grams
11% of the farmer's tomatoes have been rejected
what is the standard deviation?

i know z=(x-mean)/stdev, x=70, mean=74, P(X<70)=0.11 but i'm totally mind-blanking on how to find z and also stdev.
i think P(x<70)=P(Z<z), is that right?
any help is very much appreciated!
many thanks!!
Find the value of $z^*$ such that $\Pr(Z < z^*) = 0.11$.

From $Z = \frac{X - \mu}{\sigma}$ you therefore have $z^* = \frac{70 - 74}{\sigma}$. Substitute the value of $z^*$ and then solve for $\sigma$.

3. thanks for your reply! how do i find z* though? i'm probability-zonked
is it using normdist? or z-tables?

4. Originally Posted by lalalamaths
thanks for your reply! how do i find z* though? i'm probability-zonked
is it using normdist? or z-tables?
Use tables.

Note: Pr(Z < z*) = 0.11 => Pr(Z > -Z*) = 0.11 => Pr(Z < -z*) = 0.89. Using my old Kaye and Laby Four Figure Mathematical Tables I get -z* = 1.227 => z* = -1.277.