A city council is considering funding a proposal to create a new city park. The council...

Transcribed Image Text:

A city council is considering funding a proposal to create a new city park. The council members will fund the proposal if they conclude that more than 60 percent of the city residents support the proposal. A survey of 2,000 randomly selected city residents will be conducted to investigate the level of support for the proposal. Let X represent the number of city residents in the sample who support the proposal. Assume that X is a binomial random variable. (a) Determine the mean and the standard deviation of the random variable X, assuming that 60 percent of city residents support the proposal. The figure below shows a normal distribution that can be used to approximate the binomial probability distribution of X. The shaded region is bounded by k, and k on the figure and represents the middle 0.997 of the area under the curve. 0.997 Mean (b) Assume that 60 percent of the city residents support the proposal. Use a normal approximation and the mean and standard deviation from part (a) to determine the values of k, and k₂. (c) The survey was conducted, and 1,293 of the 2,000 city residents surveyed supported the proposal. Do your answers in part (b) and the survey results support the funding of the proposal? Justify your answer. A city council is considering funding a proposal to create a new city park. The council members will fund the proposal if they conclude that more than 60 percent of the city residents support the proposal. A survey of 2,000 randomly selected city residents will be conducted to investigate the level of support for the proposal. Let X represent the number of city residents in the sample who support the proposal. Assume that X is a binomial random variable. (a) Determine the mean and the standard deviation of the random variable X, assuming that 60 percent of city residents support the proposal. The figure below shows a normal distribution that can be used to approximate the binomial probability distribution of X. The shaded region is bounded by k, and k on the figure and represents the middle 0.997 of the area under the curve. 0.997 Mean (b) Assume that 60 percent of the city residents support the proposal. Use a normal approximation and the mean and standard deviation from part (a) to determine the values of k, and k₂. (c) The survey was conducted, and 1,293 of the 2,000 city residents surveyed supported the proposal. Do your answers in part (b) and the survey results support the funding of the proposal? Justify your answer.

Answer rating: 100% (QA)

Solution given n2000 the percentage of people who supports to the proposal is 60 Hence p06... View the full answer