Please note that this question consists of five parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question. The probability is 0.32 that the gestation period of a woman will exceed nine months. In randomly chosen six human births, let X = Number of births in which gestation period exceeds nine months from these six births. 1. What is the distribution of X? Clearly state the parameters of the distribution. 2. Write down the probability mass function, for the distribution of X. That is, write the probability mass function specific for the random variable of interest in this problem, not just the general formula.  3. What is the probability that none in the sampled 6 human births gestation period exceeds nine months? 4. What is the probability that the gestation period exceeds nine months in at least one in the sampled 6 human births? 5. Would it be unusual if the gestation period exceeds nine months in all sampled 6 human births? Show any calculation relevant to your answer.

Status of a faculty was coded as 1 if the faculty is Full Time and coded as 0 if the faculty is Part Time. The variable Status is: 

Suppose we want to estimate the population proportion p within 2% (i.e. margin of error is 2%) with confidence level of 90%. What sample size do we need to ensure this? Choose the appropriate z-multiplier for the calculation from the below provided values.

A certain city has surveyed their residents month after the Oscars 2024. Based on the data, a 90% confidence interval for the true proportion of people who watched the Oscars is 0.65

The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2004. In each class interval, the left endpoint but not the right is included, so the class intervals are [10, 15), {15, 20) etc. What percentage of universities had acceptance rates less than 25%?

The following data have been collected from 500 students on whether they are Male or Female, and whether they have a car or not: Have a car Don’t have a car Total Male 125 25 150 Female 200 150 350 Total 325 175 500 If a randomly selected student have a car, what is the probability that the student is a male?   

Please note that this question consists of four parts. You may use MINITAB to double check your final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.   A study was conducted to determine the percentage of adults in United States who are afraid to fly. Of the 1075 adults in United States surveyed, 292 were afraid to fly. Give a point estimate for the true proportion of adults in United States who are afraid to fly. The study wants to release an interval estimate for the true proportion of adults in United States who are afraid to fly. What are the conditions that need to be satisfied in order to calculate a confidence interval? Are they satisfied?  Calculate a 95% confidence interval for the true proportion of adults in United States who are afraid to fly. Interpret the interval calculated in part 3. 

A nutritionist wants to see whether a new diet will help reduce weight for women. He randomly selects 15 women and assigns them to the new diet program (length of the program is one month). For each woman, he records their weights as they start the diet and after they complete the diet program. To test whether mean reduction in weight is significant, we would do:

The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age

Student body leaders at a college want to conduct a survey to determine the proportion of students who favor a proposed honor code. Since interviewing all the students is not feasible due to practical reasons, they want to determine the sample size (number of students to be interviewed) needed to estimate the true proportion with a margin of error no larger than 5% using a 95% confidence interval. What is the sample size they need to ensure above specifications in their estimation?