The marks scored by a random sample of 40 students who did KCSE in the school are shown below

37, 55, 30, 42, 38, 40, 45, 45, 55, 65, 45, 35, 38, 32, 60, 50, 50, 48, 50, 30, 33, 40, 36, 54, 55, 50, 60, 46, 54, 48, 52, 34, 45, 60, 55, 60, 60, 50, 52, 36

determine:

(1) the 99% C. I confidence interval estimate of the population mean

(2) the 95% C.I confidence interval estimate for the proportion of students who scored more than 45 marks in the examination.

(3) the standard deviation S of the data

(4) sp

(5) the sample proportion for the students who scored more than 45 marks in the examination

(6) the sample mean X for the data

(7) the standard error of the proportion Sp= root of pq/x

(8) the standard error Sp= S/ root of n