Normal Distribution questions

Machine A fills sacks of sugar. The weights are known to be Normally distributed with a mean of 25 kg and a variance of 0.81 kg.

Machine B produces sack weights which are also normally distributed with a mean of 25.5kg and variance of 0.64kg.

A bag chosen at random weighs 26.9kg. Which machine is this bag MOST likely to have come from? (Use calculations to justify your answer)

If Z~N(5,1.44) find a)P(Z>6.2)

b)P(X<4)

Peter scores 48% in a French test and 62% in a German test. The French test had a mean of 42% and a standard deviation of 5.6%. The German test had a mean of 55% and a standard deviation of 7%.

Standardise Peters scores and say which test you judge he did better in.

The Lakes School wishes to survey number of cans of drink bought by pupils each week. A sample of 10 pupils are selected and the number of drinks they buy in one week counted.

The results are

7 10 2 6 8 8 12 0 6 10

Calculate the mean and variance of the sample.

Use these answers to provide estimates for the mean and variance of the number of drinks bought per week by all pupils

Calculate a 95% confidence interval for the mean number of drinks bought per week by all Lakes School pupils.

What do you understand by an 'unbiased estimator'

The weights of Year 8 pupils are known to have a mean of 70kg and a variance of 5kg

Find the probability that a random sample of 10 pupils will have a sample mean of less than 71kg

How large will the size of sample need to be if you are to be 95% certain that the sample mean will be in the interval 69.5-70.5kg

A sample of 200 new car tyres taken from a particular manufacturer contain 24 that are judged to be defective. Calculate a 90% confidence interval for the proportion of defective tyres produced by this manufacturer.