Soft drink bottling companies such as Coca-Cola use quality-control techniques to assure that the average amount of cola in the cans is 12 ounces. Suppose that a small standard deviation of 0.05 ounce is acceptable. Any significant difference from this standard deviation would reflect badly on the quality-control measures concerning the average amount of cola in the 12-ounce cans. A sample of size 20 indicated that the standard deviation was 0.070.

a. Determine if the standard deviation of the amount of cola in the cans differs from the standard deviation specified by the quality control division. Use a significance level of 0.10.

b. The quality-control sampling occurs several times a day. In one day, seven samples were taken, and three indicated that the standard deviation was not 0.05.

If the seven samples were taken at a time in which the standard deviation met specifications, determine the probability of having at least three out of seven samples indicate the specification was not being met.