Statistics and Probability Answers

A manufacturer knows that on average 20% of the electric toasters produced require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers x and y such that

a) the probability that at least x of them will require repairs is less than 0.5;

(b) the probability that at least y of them will not require repairs is greater than 0.8.

A manufacturer knows that on average 20% of the electric toasters produced require repairs

within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers x

and y such that

(a) the probability that at least x of them will require repairs is less than 0.5;

(b) the probability that at least y of them will not require repairs is greater than 0.8.

9.37 A study was conducted to determine if a certain treatment has any effect on the amount of metal removed in a pickling

operation. A random sample of 100 pieces was immersed in a bath for 24 hours without the treatment, yielding an average of 12.2

millimeters of metal removed and a sample standard deviation of 1.1 millimeters. A second sample of 200 pieces was exposed to the

treatment, followed by the 24-hour immersion in the bath, resulting in an average removal of 9.1 millimeters of metal with a sample

standard deviation of 0.9 millimeter. Compute a 98% confidence interval estimate for the difference between the population means.

Does the treatment appear to reduce the mean amount of metal removed?