Question

A tyre manufacturer wants to measure the inner dimension (in millimetres) of a particular type of a tyre. A sample of 12 tyres is selected and dimension is recorded as follows:

   568 572 570 571 576 573 574 578 580 584 582 587

The mean inner dimension is ___ millimetres (2 decimal places)

It is found the sample standard deviation is 5.99 millimetres. The lower limit of a 90% confidence interval for the population mean dimension (in millimetres) of tires is estimated to be _____________ (2 decimal places)

Answer 1

Mean = sum of X / n

Mean = 576.25 mm

For a 90% confidence interval, the population mean should lie between values such that z score is between 1.645 and - 1.645

Lower limit = Mean - 1.645 x std. dev. / n^0.5

Lower limit = 576.25 - 1.645 x 5.99/ 3.464 = 573.40 mm