**Question: ** Z is a standard normal random variable. Find the following probabilities.

a. P(-1.96 <= Z <+ -1.4)

b. P(Z <= +1.96)

c. (Z >= +.24)

**Question: **As part of its ongoing evaluation, HiEd University conducted a survey of current students regarding their satisfaction with their university experiences. Below is part of the resulting data.

Poor | Average | Excellent | Total | |

Less than 60 hours credit | 20 | 70 | 130 | |

60 hours or more | 30 | 20 | ||

Total | 40 | 200 |

Complete the table.

What is the probability that a student in the survey:

a) gave an excellent rating?

b) did not give a poor rating?

c) gave a poor rating or had 60 hours of credit or more?

d) gave an excellent rating if they had less than 60 hours of credit?

** Question: ** Two unrelated participants were selected randomly from the population summarized in the table below. One non-hypertensive female and one hypertensive male were selected. Find a chance that exactly one of the selected people is diabetic.

HYPERTENSIVE | GENDER | % DIABETICS |

YES | F | 25% |

YES | M | 35% |

NO | F | 5% |

NO | M | 10% |

P =

**Question: **(8 marks). Researchers at Leeds University School of Dentistry want to know whether registering with a NHS dental practice or a private dental practice will make a difference in children’s regular check-ups. Consider the table of data collected:

Dental practice | Regular check-ups | Non-regular check-ups | Total |

private | 201 | 50 | 251 |

NHS | 985 | 375 | 1360 |

Total | 1186 | 425 | 1611 |

a. What is the proportion of children that have registered with NHS dental practice? (1 marks)

b. What is the proportion of children that have registered with private dental practice? (1 marks)

c. What is the proportion of children that have registered with NHS dental practice in the group of regular check-ups? (1 marks)

d. What is the proportion of children that have registered with private dental practice in the group of regular check-ups? (1 marks)

e. What is the absolute difference in the proportions of that have registered with NHS dental practice in the group of regular check-ups, compared to the group of non-regular check-ups. (1 marks)

f. Conduct a chi-square test with null hypothesis that there is no association between dental practice and regular check-ups. What is your conclusion? (3 marks)

**Question: ****In a month long study of a daily dose of an experimental anxiety drug, some of the 250 ****subjects experienced headaches. Using the following computer results from the study, find the probability of randomly selecting a study subject that had experienced**

X | 0.00 | 1.00 | 2.00 | 3.00 | 4.00 | 5.00 | 6.00 |

P(X) | 0.3341 | 0.4019 | 0.2014 | 0.0538 | 0.0081 | 0.0006 | 0.0000 |

**X = number of headaches**

**a. ****At least five headaches.**

**b. ****At most two headaches.**

**c. ****More than one headache.**

**d. ****At least one headache.**

**Question: ****A test consists of multiple-choice questions, each having four possible answers with ****only one being correct. Assume that you guess the answers to six such questions.**

**a. ****Find the probability that the first two guesses are wrong and the last four guesses are correct.**

**b. ****Determine the number of different possible arrangement of two wrong answers and four correct answers.**

**c. ****What is the probability of getting exactly four correct answers when six guesses are made?**

**Question: ****BINGO involves drawing labeled ping pong balls at random without replacement ****from a hopper. There are 75 balls with 15 for each of the letters B, I, N, G and O. What is the probability of drawing**

**a. ****Two G balls in the first two selections?**

**b. ****Three B balls in the first three selections?**

**c. ****An I ball followed by a N ball followed by an O ball in the first three selections?**

**d. ****An I, N and O ball in any order in the first three selection? NOTE: 18c and 18d are asking different questions; thus, they yield different answers.**

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