About 27 I just knew how to get mean, I stuck on how to get S.D. Plz answer all

Question

About 27 I just knew how to get mean, I stuck on how to get S.D.

Plz answer all the questions, show me the R code if you can.

Thanks!

Use the Following Text for Questions 27-29 A University published that 7.7% of the students in the freshmen class of 2020 are international students To investigate this claim, a simple random sample of 500 University students in the class of 2020 was obtained. 27. According to the Central Limit Theorem, what's the distribution of this sample proportion. p? Specify the shape, mean, and standard deviation. You must show all work in order to receive full credit. Round your final answers to 4 decimal places as needed. (3 points) 29. Find the probability that between 5% and 10% of these students are international students You must show all work (including R Code and output in order to recei ve full credit (3 points) 30. Find the 65th percentile for the proportion of these students that are international students You must show all work (including R Code and output) in order to receive full credit. (3 points)

Explanation / Answer

Proportion ( P ) =0.077

Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.077*0.923/500) = 0.01192

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