A tourism magazine surveyed 5,000 people for their expected travel plans in the following year. The response rate of the survey is seventy-five per cent. Forty-five per cent of the respondents of the survey agreed that they already have plans for their visits in the following year, while the remaining respondents said that they like to plan spontaneously. Assume that while preparing a research report for your hospitality class you conduct a similar survey and select a sample of 40 people.

a. Calculate the probability that the proportion that plans their visit in advance lies between 43% and 47%.

b. Calculate the probability that proportion that plans their visit in advance is less than 60%.

c. Determine the confidence interval that the proportion mean is 60% given the 90% level of confidence.

d. Determine the confidence interval that the proportion mean is 45% given the 90% level of confidence.