1. Assuming that the diameters of 1000 brass plugs taken consecutively from a machine, form a normal distribution with mean 0.7515 cm and standard deviation 0.0022 cm. How many of the plugs are likely to be rejected if the approved diameter is 0.752± 0.004.

2. A machinist is making engine parts with axle diameter of 0.7 inch. A random sample of 15 parts shows mean diameter 0.742 inch with a standard deviation of 0.04 inch. On the basis of this sample would you say that the work is inferior?

3. A random sample of size 56 from a normal population showed a mean of 63 and a sum of squares of deviation from the mean equals to 180. Can this sample be regarded as taken from the population having 65 as mean at 1% level of significance?