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**puccinitang****Guest**

Help me plz, thanks

A teacher claims that the time (in minutes) required for any HKU student to finish the homework is a normally distributed random variable with a mean of 30 minutes and a standard deviation of 10 minutes.

(i) If a student is randomly selected from HKU, what is the probability that he/she will use more than 27 minutes but less than 32 minutes to finish the homework?

(ii) If a sample of 6 students is randomly selected from HKU, find the probability that the average time of 6 students to finish the homework will be more than 32 minutes?

(iii) Suppose the time (in minutes) required to finish the homework is not a normal random variable. Under what circumstances can part (b) still be evaluated?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,366

Hi;

i) P(27 < X <= 32) = .1972

Under what circumstances can part (b) still be evaluated?

Where is part b?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**puccinitang****Guest**

sorry, part b= part ii

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,366

Hi;

ii) .3121

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**puccinitang****Guest**

how about iii?

help me please /_\

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,366

Hi;

iii) The question is way too general and requires making too many assumptions. If I draw at random from a distribution of any shape and I draw a big sample then the distribution of the sample will approach a normal distribution. They usually pick n = 30.

If I draw a sample of 6 students from this unknown distribution then I will have great difficulty with ii)

The general answer for iii) is that I can get the answer if I know the distribution or if the random sample is 30 or more. This is the best I can do.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**puccinitang****Guest**

thank you very much

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,366

Hi;

Hope that was okay and welcome to the forum.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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