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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 standard deviation of the random variable X, assuming that 60 percent of city residents support the proposal
B. Assume that 60 percent of city residents support the proposal. Use a normal approximation and the mean and standard deviation from part a to determine the values of k1 and k2 (the left and right boundaries of the middle .997 area)
C. The survey was conducted, and 1293 of the 2000 city residents supported the proposal. Do your answers in part b and the survey support the funding of the proposal? Justify your answer.

Respuesta :

The mean and standard deviation of the random variable X if 60 percent of city residents support the proposal is 1200 and 21.9 respectively.

How to calculate the mean?

From the information given, the mean of the binomial variable x will be:

= 2000 × 60%

= 2000 × 0.6

= 1200

The standard deviation will be:

= ✓n × ✓p(1 - p)

= ✓1200 × ✓0.4

= ✓480

= 21.9

Also, the mean and standard deviation to determine the values of k1 and k2 will be -3 and 3.

Lastly, the test statistic will be:

= (0.65 - 0.60)/(✓0.60 × (0.40) /2000

= 0.05/✓0.24/2000

= 0.05/0.011

= 4.55

The z value at 5% significance level is 1.64. This supports the funding of the proposal.

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