Help with this R Software question?? (Statistics) Please help with Question 4 on

Question

Help with this R Software question?? (Statistics) Please help with Question 4 on the image provided. For ease of time, I have provided the answers to question 3:

3. a) pnorm(60,54,6.2785)

[1] 0.8303735

b) pnorm(55,54,6.2785)-pnorm(30,54,6.2785)

[1] 0.5632074

c) pnorm(50,54,6.2785)

[1] 0.2620315

Chapter 8. Statistical Com Chapter 8. Statiscal Computing Lab 188 puting Labs to give P(X ). For example, pnorm (1.96,mea 0.975 (or more exactly, 0.975002 intervals. norm ( 1.96,mean=0,sd=1) yields 1), which is used for 95% confidence 3. Suppose that 27% of the population has high blood pressur random sample of 200 people, what is the exact probability (to, decimal places) that e. In a hat is the exact probability (to, say, (a) less than 60 people have high blood pressure? (b) more than 30, but less than 55, of the people selected have high blood pressure? (c) more than 150 people do not have high blood pressure? Include your R code and output in your lab report for parts (a), (b) and (c) above. 4. Answer Question 3(b) above using the normal approximation to the binomial, remembering to use the continuity correction. Use the pnorm function described above and include your R code and output in your lab report. How well did the approximation perform?

Explanation / Answer

For qs 3 you cannot use normal approximation as it is asked in the question to find the exact probability. So you have to do it by binomial distributiion. For that use the function pbinom in R with n=200 and p=0.27. For qs 4 you have to use normal approximation with mean=np and variance=npq and there you use the function pnorm.

Here for the qs 3(b) using pbinom, the exact probability comes out to be 0.5987967

and using pnorm, the normal aproximated probablity comes out to be 0.5632074.

So if you take upto one decimal place the approximation performs well but after that it doesnot perform well.

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