S2 sampling (+rep available!)

I really don't know what to do with these qs and would love some guidance; stats is just hopeless atm :frown:

I'm not expecting anyone to do all of these, but maybe if someone could show me what to do for one of them I'll know how to do the others!

They are quite wordy though so I apologise in advance:

1. 30 apples are chosen at random from a large box of Braeburn apples. Their masses, x grams, are summarised by sum x = 3033 and sum (x^2) = 306676. [Find, to 4 sig figs, unbiased estimates for the mean and variance of the mass of an apple in the box (done this: got 101.1g for the mean and 1.369g^2 for the variance.)] The apples are picked in bags of 10 in a shop and the shopkeeper told customers that most bags weigh more than 1kg. Show that the shopkeeper's statement is correct, indicating any necessary assumption made in your calculation.

2. A machine is set to produce ball-bearings with mean diameter 1.2cm. Each day a random sample of 50 ball-bearings is selected and the diameters accurately measured. If the sample mean diameter lies outside the range 1.18cm to 1.22cm then it will be taken as evidence that the mean diameter of the ball-bearings produced is not 1.2cm. The machine will then be stopped and adjustments be made to it. Assuming that the diameters have standard deviation 0.075, find the probability that:
a) the machine is stopped unnecessarily;
b) the machine is not stopped when the mean diameter of the ball-bearings produced is 1.15cm.

3. The number if night calls to a fire station serving a small town can be modelled by a Poisson distribution with mean 2.7 calls per night.
a) State the expectation and variance of the mean number of night calls over a period of n nights.
b) Estimate the probability that during a given year of 365 days the total number of night calls will exceed 1050.

Thanks to anyone who can help!

Reply 1

OCC++

Qns 3 is the easiest to answer:P
part a is about a concept involved in Poisson Distribution, that a mean in a time interval is proportional to the time interval. for example the mean for 2 nights long will be 5.4 .

Qns 1...
ok first you have to account for the bags of 10. Modify the normal distribution for an apple to that of 10 apples (check your notes if you really don't know or pm me if you lost your notes).'I believe you know the standard assumption.

Qns 2 ...
use central limit theorem to find the normal distribution of the sample mean of the 50balls.

Reply 2

sharingissexy

1- P(1.18 < Xbar < 1.22)
=1-P((1.18-1.2)/(0.075/surd(50)) < Xbar <(1.22-1.2)/(0.075/surd(50))
=1-P(-1.8856 < X bar < 1.8856)
=1- 0.94066
=0.05934
hope this helps u :colondollar:

Reply 3

blacklistmember

you dont have rep though :smile:

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