A random sample of 500 apples was taken from large consignment and 45 of them were found to be bad. Find the limits at which the bad apples lie at 99% confidence level.

A sample of five measurements of the diameter of a sphere were recorded by a scientist as 6.33, 6.37,6.36,6.32 and 6.37 mm. Determine the point estimate of
(a) mean
(b) variance.

A random sample of marks in mathematics secured by 50 students out of 200 students showed a mean of 75 and a standard deviation of 10. Find the 95% confidence limits for the estimate of their mean marks.

A company market car tyres. Their lives are normally distributed with a mean of 50,000 kms and standard derivation of 2000 kms. A test sample of 64 tyres has a mean life of 51250 km. Can you conclude that the sample mean differs significantly from the population mean? (Test at 5% level).

The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 825 hours with the S.D. of 110 hours. If II is the mean life time of all the bulbs produced by the company, test the hypothesis that μ = 900 hours at 5% level of significance.