Question

According to the Centers for Medicare & Medicaid Services, 16% of nursing homes received five stars in overall ratings in 2011. A random sample of six nursing homes was selected. What is the probability that two or three of them received five stars?

Question 7 options: 0.1310 0.2019 0.2398 0.4350

Question 8) Assume that the number of pieces of junk mail per day that a person receives in their mail box follows the Poisson distribution and averages 3.5 pieces per day. What is the probability that this person will not receive any junk mail tomorrow?

Question 8 options: 0.0302 0.0514 0.1018 0.1698

Question 9) Dwight Howard plays center for the Orlando Magic in the National Basketball Association and averaged 2.4 blocked shots per game during the 2011 season. Assume that the number of blocked shots per game follows the Poisson distribution. What is the probability that Dwight Howard will block exactly four shots during the next game?

Question 9 options: 0.0747 0.1254 0.2366 0.3218

Question 10 (5 points) Which of the following is not a condition of a discrete probability distribution?

Question 10 options:

a) Each outcome in the distribution needs to be mutually exclusive with other outcomes in the distribution.

b) The probability of a success must exceed the probability of a failure.

c) The probability of each outcome, P(x), must be between 0 and 1 (inclusive).

d) The sum of the probabilities for all the outcomes in the distribution needs to add up to 1.

Answer #1

7)

here this is binomial with parameter n=6 and p=0.16 |

probability that two or three of them received five stars:

P(2<=X<=3)= |
∑_{x=a}^{b }
(_{n}C_{x})p^{x}(1−p)^{(n-x) }
= |
0.2398 |

8)

this is Poisson distribution with parameter λ=3.5 |

probability that this person will not receive any
junk mail tomorrow =e^{-3.5} =**0.0302**

9)

this is Poisson distribution with parameter λ=2.4 |

probability that Dwight Howard will block exactly four shots during the next game:

P(X=4)= |
{e^{-λ}*λ^{x}/x!}= |
0.1254 |

10)

**b) The probability of a success must exceed the
probability of a failure.**

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