Question

According to a study, 80% of married people hide purchases from their mates. A random sample of 20 randomly selected married people is taken. 31. Use Minitab to calculate the probability that exactly 19 of the 20 randomly selected married people hide purchases from their mates. (2 points) 32. Use Minitab to calculate the probability that 19 or more people hide purchases from their mates. (2 points) 33. Use Minitab to calculate the probability that fewer than 12 people hide purchases from their mates. (2 points) The mean number of pages that a certain toner cartridge can print is 4302, with a standard deviation of 340. Assume that the number of pages that a cartridge will print is normally distributed. 35. Use Minitab to find the probability of a toner cartridge printing between 3500 and 4500 pages. (2 points) 36. Use Minitab to find the probability of a toner cartridge printing fewer than 4000 pages. (2 points)

Answer 1

The distribution follows a binomial distribution with n=20, p=0.8, q=0.2

The values of the probabilities for various values of X are as below:

X	p(X)
0	1.04858E-14
1	8.38861E-13
2	3.18767E-11
3	7.65041E-10
4	1.30057E-08
5	1.66473E-07
6	1.66473E-06
7	1.33178E-05
8	8.65659E-05
9	0.000461685
10	0.002031414
11	0.007386959
12	0.022160877
13	0.05454985
14	0.109099701
15	0.174559522
16	0.218199402
17	0.205364143
18	0.136909429
19	0.057646075
20	0.011529215

31. P(X=19) = C[20,19] x 0.8¹⁹ x 0.2¹ = 0.0576

32. P(X>=19) = P(X=19) + P(X=20) = 0.0576 + 0.0115 = 0.0691

33. P(X<12) = 0.00998 ~ 0.01