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**Unknown1729=sumof2cubes****Guest**

Prove 1+1=2, I wish to know the reason behind this simple arithmetic operation from the axioms of set theory.

**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 27,883

Hi,

Please see the link : Peano axioms.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**monie27****Member**- Registered: 2019-03-13
- Posts: 5

Hi.I am struggling with the following questions.

Anyone perhaps good with Business Statistics?Please help if you can.The scenario and question is as follow.

A coffee dispensing machine used in most cafeterias is set to dispense coffee with an average fill of 230 ml and a variance of 100ml per cup. Assuming the volume dispensed is normally distributed, calculate the following (rounded to three decimals):

(a) The probability of the dispenser filling a cup to more than 235 ml. (3)

(b) The probability of the dispenser filling a cup between 235 and 245 ml. (4)

(c) If 350 cups were filled by this coffee dispenser, what is the expected number of cups that will be filled to less 235 ml

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**Grantingriver****Member**- Registered: 2016-02-01
- Posts: 129

Hi monie27, you should make more practice with the nomal distribution problem since this question is a standatd question about this distribution. However, there are to ways to solve this question the first one by calculating the probabilities directly from the probability density formula, but the second and more common way to calculate the required probabilities is by using the normal distribution tables. I will solve the problem by the second method as an illustration as below:

You first have to deduce the standard deviation which is the squre root of the variance, so from the given infronation its value is 10 ml. Second you have to measure the filling amount of coffee in terms of the standard deviation after putting the normal distribution in the standard form (i.e. putting the average of the filling amount of coffee equals to zero). Therefore, applying the previous procedures, the required answers are:

a- (235-230)/10=0.5 ⇒ 1-0.6915=0.3085

b- (245-230)/10=1.5 ⇒ 0.9332-0.6915=0.2417

c- 350×0.6915=242.025 cups

Good luck

*Last edited by Grantingriver (2019-04-03 07:19:40)*

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**monie27****Member**- Registered: 2019-03-13
- Posts: 5

Hi Grantingriver, thank you for the assistance on my previous question. I now also have a question related to interval estimation.

The information is as follow:

In 1938, the first bottling company opened in Johannesburg and the Coca-Cola Export Corporation set up a permanent operation in South Africa, with plants being built in Auckland Park and Durban. The first bottling operation to open in Cape Town was in Paarden Eiland in 1940. Today, over 12 000 people in South Africa, work for Coca-Cola. The inspection division of Peninsula Beverages Weights and Measures Department is interested in estimating the actual amount of soft drink that is placed in their 2-litre bottles at the local bottling plant in Cape Town. The bottling plant has informed the inspection division that the standard deviation for 2-litre bottles is 0.05 litres. A random sample of 100 2-litre bottles obtained from this bottling plant indicates a sample average of 1.99 litres.

How do I find the

a) a 95% confidence interval for the population mean (u).

b) he length of the confidence interval.

Thanking anyone for you response and help or guidance in advance!

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 691
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Hi **monie27**. Welcome to Math Is Fun Forum.

In future, if you have a question, please start your own thread, instead of hijacking an existing thread. This is the second time you’ve done it.

Thank you. Have a good day.

Me, or the ugly man, whatever (3,3,6)

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