Please give me step by step solutions thank you A machine op

Please give me step by step solutions, thank you!

A machine operation produces widgets whose diameters are normally distributed, with a mean of 4.97 inches and a standard deviation of 0.06 inches. Suppose that specifications specifications require that the widget diameter be 5.00 inches plus or minus 0.12 inches (that is, between 4.88 and 5.12 inches).

After a disgruntled employee kicked the machine, the mean shifted to 4.91 inches, and the standard deviation shifted to 0.10 inches, while the distribution of the diameters remained normal.

a) What proportion of the production will be unacceptable after the machine is kicked?

b) After the machine was kicked, 25 widgets are independently and randomly selected from the production process. What is the probability that at least 7 of the 25 will be unacceptable?

c) After the machine was kicked, what is the probability that the production process will be stopped after examining a random sample of 25 widgets?

Solution