Help in H2 maths - statistics? replied by secretliker @ Thu, 12 Jun 2008 00:54:04 +0800

secretliker — Thu, 12 Jun 2008 00:54:04 +0800

1) A computer repair company uses a particular spare part at an average rate of 5 per week. It is assumed that the request for the spare part occurs randomly and independently.

i) The manager decides to replenish the stock of this particular spare part to a constant level k at the beginning of each week. Find the least value of k such that on average there will be insufficient stock no more than once in a 26-week period.(k=9)

Let X be the average rate at which the company uses a particular spare part in 1 week.

X~Poi(5)

This simply means the average rate at which the company is using.

Now, k is the number of spare parts at the beginning of each week.

To have insufficient stock, the probability is P(X>k) = 1-P(X<=k)

Using GC (I don't know about TI but my CASIO fx-9860G could do it), generate a list of 1 - P(X<=k)

Now generate another list of 26[1-P(x<=k)]

You'll see that k is 9, where 26[1-P(x<=K)] is below 1.

2)An internet service provider serves 5000 subscribers and during off peak period, there is a probability of 0.04 for each subscriber that he requires a line for a correction.

Using a suitable approximation, find the least number of lines required to be set up by the internet service provider such that the probability that a connection will fail during an off peak period due to all the lines being occupied is less than 1%.(232)

Let X is the number of subscribers that requires a line for a correction out of 5000 during an off peak period.

X~Bin(5000,0.04)

Since np > 5, nq > 5, npq > 5, X can be approximated to a normal distribution.

X~N(np, npq)

X~N(200, 192)

P(X>a) < 0.01, where a is the number of lines set up.

Remember to apply continuity correction. P(X>a+1) = P(X>a+0.5)

Using GC, a+0.5 = 232.234822

a=231.734822

By looking at the normal distribution curve (important), and since number of lines is a whole number, the least number is 232.

Help in H2 maths - statistics? replied by RETARDED_MORON @ Tue, 10 Jun 2008 12:09:17 +0800

RETARDED_MORON — Tue, 10 Jun 2008 12:09:17 +0800

Use your GC!

Don't forget to reset your GC though.

Help in H2 maths - statistics? replied by Something random @ Tue, 10 Jun 2008 02:10:27 +0800

Something random — Tue, 10 Jun 2008 02:10:27 +0800

1) This question I don't understand what they are asking. So instead I'm using the answer k=9 and trying to work with that... and still cannot get the right answer lol. Just showing my workings below.

Looks like a Poisson distribution to me.

Let the no. of requests for spare parts be X.

X~Po(5)

P(Insufficient stock)

= P(X>k)

= 1 - P(X<=k) ***1 - [poissoncdf (5,k)]***

= Ans

Let the no. of times there is insufficient stock in a 26-week period be Y.

Y~B(26,Ans)

P(Y<=1) > ? ***binomcdf (26,Ans,1)***

The last part, I don't know what the question means by "on average".

2) Have to use normal approximation from binomial.

X~B(5000,0.4)

=> X~N(200,192) approximately

P(Z>a) < 0.01

P(Z<=a) > 0.99

***invNorm(0.99,200,sqrt192)***

= 232.235

Help in H2 maths - statistics? replied by thousandisland @ Tue, 10 Jun 2008 00:24:08 +0800

thousandisland — Tue, 10 Jun 2008 00:24:08 +0800

yeah and i gotta take stats exemption test somemore. mati.

Help in H2 maths - statistics? replied by sinicker @ Tue, 10 Jun 2008 00:04:43 +0800

sinicker — Tue, 10 Jun 2008 00:04:43 +0800

i loved stats.

but after 2 years of NS, those words just dont make sense to me anymore.

die, uni in 2mths time i'm DEAD.

Help in H2 maths - statistics? replied by eagle @ Tue, 10 Jun 2008 00:02:10 +0800

eagle — Tue, 10 Jun 2008 00:02:10 +0800

I hate stats

yucks

Help in H2 maths - statistics? replied by lavastar @ Mon, 09 Jun 2008 23:53:39 +0800

lavastar — Mon, 09 Jun 2008 23:53:39 +0800

1) A computer repair company uses a particular spare part at an average rate of 5 per week. It is assumed that the request for the spare part occurs randomly and independently.

i) The manager decides to replenish the stock of this particular spare part to a constant level k at the beginning of each week. Find the least value of k such that on average there will be insufficient stock no more than once in a 26-week period.(k=9)

2)An internet service provider serves 5000 subscribers and during off peak period, there is a probability of 0.04 for each subscriber that he requires a line for a correction.

Using a suitable approximation, find the least number of lines required to be set up by the internet service provider such that the probability that a connection will fail during an off peak period due to all the lines being occupied is less than 1%.(232)

Thx to those who can help. Sometimes i cannot understand this qns as they are so wordy