Question

A random sample of 10 examination papers in a course, which was given or fail basis, showed the following scores. (PAPER NUMBERS) (GRADES) (STATUS) 1 85 Pass 2 87 fail 3 92 Pass 4 85 Fail 5 79 Pass 6 90 Pass 7 88 Fail 8 74 Pass 9 79 fail 10 91 pass 1. estimate the probability that the grade will be more than 85. 2. estimate the probability that the proportion of fail will be less than 0.65. 3. Estimate the 97% confidence interval for grade. 4. Estimate the interval of proportion for pass at the 98% confidence level.

Answer 1

(a)

Out of 10 scores, 5 are more than 85 so the probability that the grade will be more than 85 is

P(more than 85) = 5/10 = 0.50

2:

Out of 10, 4 were fail so

P(fail) = 4/10 = 0.40

So the probability that the proportion of fail will be less than 0.65 is 1.0000.

3;

Here we need to find the 97% confidence interval for grade so we need to find mean and standard deviation of grade. Following are the descriptive statistics is

4:

Out of 10, 6 were pass.