A random sample of 10 examination papers in a course, which was given on a pass

Question

A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores.

Paper Number /Grade /Status

1 65 Pass

2 87 Pass

3 92 Pass

4 35 Fail

5 79 Pass

6 100 Pass

7 48 Fail

8 74 Pass

9 79 Pass

10 91 Pass

1. The point estimate for the mean of the population is

2. The point estimate for the standard deviation of the population is

3. The point estimate for the variance of the population is

4. The point estimate for the proportion of all students who passed the ciurse is

Explanation / Answer

1.
Point estimate of the mean = sum of grades/10
xbar = 750/10 = 75

2.

Variance = 3776/(10-1) = 419.56

std. dev. = sqrt(419.56) = 20.48

point estimate of std. dev. s = 20.48

3.

Point estimate of variance, s^2 = 419.56

4.

Out of 10, 8 passed the course

Hence point estimate, pcap = 8/10 = 0.8

x (x-xbar)^2 65 100 87 144 92 289 35 1600 79 16 100 625 48 729 74 1 79 16 91 256 Sum 3776

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