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Normal Distribution

Jam is sold in jars and the mean weight of the contents is 108 grams. Only 3% of jars have contents weighing less than 100 grams. Assuming that the weight of jam in a jar is normally distributed find:

a) the standard deviation of the weight of jam in a jar

b) the proportion of jars where the contents weigh more than 115 grams.

c) Find the probability that 2 or fewer jars have contents weighing more than 115 grams

I can do parts A and B but im having some trouble with part C, can anybody help?
Maths question.PNG72.5KB
Reply 1
Avatar for Pangol
Pangol
15
Original post by Apachee69
Jam is sold in jars and the mean weight of the contents is 108 grams. Only 3% of jars have contents weighing less than 100 grams. Assuming that the weight of jam in a jar is normally distributed find:

a) the standard deviation of the weight of jam in a jar

b) the proportion of jars where the contents weigh more than 115 grams.

c) Find the probability that 2 or fewer jars have contents weighing more than 115 grams

I can do parts A and B but im having some trouble with part C, can anybody help?


The crucial bit of (c) is that this is a sample of 25 jars. If you have done (b), you'll know the probability of a single jar having a weight of more than 115 g. The situation in (c) needs the use of a different probability distribution, one where you know the number of trials (25), where you have a fixed probability of being > 115 g, where you are only interested in two outcomes (> 115 g or not)... I hope you can see the distribution you need to use!
Original post by Apachee69
Jam is sold in jars and the mean weight of the contents is 108 grams. Only 3% of jars have contents weighing less than 100 grams. Assuming that the weight of jam in a jar is normally distributed find:

a) the standard deviation of the weight of jam in a jar

b) the proportion of jars where the contents weigh more than 115 grams.

c) Find the probability that 2 or fewer jars have contents weighing more than 115 grams

I can do parts A and B but im having some trouble with part C, can anybody help?


From part b) you have the probability that a given jar has contents weighing more than 115 grams.

For c) we're looking at the distribution of the number of jars with contents more than 115 grams from a sample of 25.
So, sample size of 25, and fixed probability of "success" for any given observation. What distribution does that suggest?
Reply 3
Avatar for Apachee69
Apachee69
OP
2
Original post by ghostwalker
From part b) you have the probability that a given jar has contents weighing more than 115 grams.

For c) we're looking at the distribution of the number of jars with contents more than 115 grams from a sample of 25.
So, sample size of 25, and fixed probability of "success" for any given observation. What distribution does that suggest?

I initially used the information to do a binomial distribution but it gave quite a high probability so i was insure if my method was corrrect?
Reply 4
Avatar for Pangol
Pangol
15
Original post by Apachee69
I initially used the information to do a binomial distribution but it gave quite a high probability so i was insure if my method was corrrect?

That's certainly the right idea. If you're worried that you haven't got it right, show us your working and we can suggest any changes you might need to make (although you might be right!).

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