1. According to the Centers for Medicare & Medicaid Services, 21% of nursing hom
ID: 3332124 • Letter: 1
Question
1. According to the Centers for Medicare & Medicaid Services, 21% of nursing homes in the United States received five stars in overall ratings on a scale of 1 to 5. A random sample of seven nursing homes was selected. What is the probability that two or three of them received five stars?
0.2226
0.4112
0.2381
0.1457
2, According to the Centers for Medicare & Medicaid Services, 21% of nursing homes in the United States received five stars in overall ratings on a scale of 1 to 5. A random sample of seven nursing homes was selected. What is the mean of this distribution?
0.85
0.40
1.47
1.97
0.2226
0.4112
0.2381
0.1457
Explanation / Answer
1)
Probability that selected nursing home is rated 5 stars = 0.21 or 21%
Probability that selected nursing home is not rated 5 stars = 1-0.21 = 0.79
sample size selected = 7
probability that two or three of them received five stars = probability that two of them received five stars + probability that three of them received five stars
probability that two of them received five stars = 7C2(0.21)2(0.79)5 = 0.2850
probability that three of them received five stars = 7C3(0.21)3(0.79)4 = 0.1262
probability that two or three of them received five stars = 0.2850+0.1262 = 0.4112
probability that two or three of them received five stars = 0.4112
2)
Probability that selected nursing home is rated 5 stars = 0.21 or 21%
Probability that selected nursing home is not rated 5 stars = 1-0.21 = 0.79
sample size selected = 7
mean of this distribution = np = 7*0.21 = 1.47
mean of this distribution = 1.47
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