**Question: **Consider the following probability distribution:

x | P(X=x) |

2 | .15 |

3 | .35 |

5 | .40 |

6 | .10 |

What is the standard deviation of X? (Points: 15)

** **

**Question: ** As a company manager for Claimstat Corp., there is a .40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion, a

raise, or both. The probability of getting a promotion and a raise is 0.25.

a. If you get a promotion, what is the probability you will also get a raise?

b. What is the probability you will get a raise?

c. Are getting a raise and getting a promotion independent events? Explain using probabilities.

d. Are these two events mutually exclusive? Explain using probabilities.

**Question: ** The sales records of a real estate agency show the following sales over the past 200 days:

Number of Houses Sold | Number of Days |

0 | 60 |

1 | 80 |

2 | 40 |

3 | 16 |

4 | 4 |

a. Assign probabilities to the sample points and show their values.

b. What is the probability the agency will sell one house in a given day?

c. What is the probability the agency will sell fewer than three houses in a given day?

d. What is the expected number of houses sold on any given day?

**Question: **Suppose that 9 female and 7 male applicant have been successfully screened for 5 positions. If the 5 positions are filled at random from the 16 finalists, what is the probability of selecting

A. 3 females and 2 males

B. 4 females and 1 male

C. 5 femalesD. at least 4 females

** Question: ** In certain community the prevalence of hypertension (HT) among three groups (N-normal, P-prediabetic, D-diabetic) are reported in Table 1, while Table 2 presents cross-tabulation of gender and diabetic status for the same community.

a) One person is randomly selected from the community. Find probability that this person is female.

b) One person is randomly selected and it appears that this person is pre-diabetic and is not hypertensive. Find probability that this person is female.

** Question: ** Health status of UNCC students was investigated in the research study. The distribution of fasting glucose (FG) was approximately normally distributed with mean 97 and standard deviation of 10. During 12 days, a sample of fifty students was selected. What is the probability that at least 6 students have FG < 87? Selected values of CDF (cumulative probabilities) for Binomial distributions are below. Please, justify your answer.

__p n k P(X≤k)____

0.16 6 2 0.94396

0.16 6 3 0.99252

0.16 6 4 0.99945

0.16 6 5 0.99998

0.16 12 2 0.70100

0.16 12 3 0.88863

0.16 12 4 0.96904

0.16 12 5 0.99355

0.16 12 6 0.99900

0.16 12 7 0.99988

0.16 50 2 0.00900

0.16 50 3 0.03117

0.16 50 4 0.08078

0.16 50 5 0.16773

0.16 50 6 0.29194

0.16 50 7 0.44065

0.68 6 2 0.08749

0.68 6 3 0.29356

0.68 6 4 0.62198

0.68 6 5 0.90113

0.68 12 2 0.00037

0.68 12 3 0.00281

0.68 12 4 0.01445

0.68 12 5 0.05401

0.68 12 6 0.15210

0.68 12 7 0.33077

0.68 50 24 0.00263

0.68 50 25 0.00612

0.68 50 26 0.01326

0.84 6 2 0.00748

0.84 6 3 0.05604

0.84 6 4 0.24722

0.84 6 5 0.64870

0.84 12 3 0.00001

0.84 12 4 0.00012

0.84 12 5 0.00100

0.84 12 6 0.00645

0.84 12 7 0.03096

** Question: ** During typical 5 years the average number of new cancer cases of certain type in Charlotte was 60. Assume that the number of new cancer cases can be well modeled using Poisson distribution. If conditions for the disease are similar during 2014, how high is the chance that 10 or more cases will be observed this year (use table on next page )? Justify your answer.

k µ=6 µ=12 µ=24

0 0.00248 0.00001 3.7751E-11

1 0.01735 0.00008 9.4378E-10

2 0.06197 0.00052 .000000012

3 0.15120 0.00229 .000000099

4 0.28506 0.00760 .000000621

5 0.44568 0.02034 .000003126

6 0.60630 0.04582 .000013146

7 0.74398 0.08950 .000047500

8 0.84724 0.15503 .000150563

9 0.91608 0.24239 .000425397

10 0.95738 0.34723 .001084999

11 0.97991 0.46160 .002524130

12 0.99117 0.57597 .005402392

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