# Normal distribution with probability from random sample

#### Jonny99

##### New member
Hi all!

I have an exam tomorrow and one of the sample questions I have been given is...

The weights of apples in an orchard are normally distributed with mean = 120 grams and standard deviation = 9 grams.
What is the approximate probability that a random sample of 81 apples will weigh under 9000 grams?

I understand it until the second line that asks about the probability, if any one could provide me with a method/formula to solve this I'd really appreciate it. I have already Googled for about 2 hours with no results for a question worded like this. Thanks in advance! Jonny

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#### Subhotosh Khan

##### Super Moderator
Staff member
Hi all!

I have an exam tomorrow and one of the sample questions I have been given is...

The weights of apples in an orchard are normally distributed with mean = 120 grams and standard deviation = 9 grams.
What is the approximate probability that a random sample of 81 apples will weigh under 9000 grams?

I understand it until the second line that asks about the probability, if any one could provide me with a method/formula to solve this I'd really appreciate it. I have already Googled for about 2 hours with no results for a question worded like this. Thanks in advance! Jonny Have you learned about z-transformation of normally distributed data?

#### Dr.Peterson

##### Elite Member
You might be after something like this (or maybe not). The numbers at the bottom show standard deviation difference from the mean and the percentages show how likely you fall into that area View attachment 10771
The numbers at the bottom are called z; presumably you know how to calculate z knowing x, mu, and sigma, or else you can just count standard deviations.

The big question is, is this all you have for finding probabilities (for the specific values of x in the picture), or do you also have access to a table or computer program or something that gives probabilities for other values of z?

If all you have is the graph, then you can (hopefully) approximate the numbers you need on the graph.

The even bigger question is, do you know about the standard deviation of the distribution of sample means? (Or anything else about samples, if such a term hasn't been used?)

#### Subhotosh Khan

##### Super Moderator
Staff member
You might be after something like this (or maybe not). The numbers at the bottom show standard deviation difference from the mean and the percentages show how likely you fall into that area View attachment 10771
You are correct!