1.Fail: 15% Pass:40% Credit:25% Distinction:15% High Distinction:5%

A grade point of 7 is assigned to each High Distinction, 6 to each Distinction, 5 to each Credit, 4 to each Pass, 0 to each Fail.

a) if a. random sample of 15 results is selected, the probability of at least one Distinction or High Distinction is?

b) The average of the grade points for the course is?

c) The variance of the grade point for this course is?

2.The survey shows that 25% of visitors through safety is a key reason for them in choosing Japan as their travel place. If you asked to conduct a follow-survey in order to provide 99% confidence that the point estimate is correct to within a margin of error of 0.02

How large a sample size is required?

3.took a sample of 13 batteries

342 426 317 545 264 451 1049 631 512 266 492 562 298

the firm has proposed a null hypothesis: the mean life of the batteries is less than or equal to 400hours

a) At the 0.05 level of significance, what the critical value that the manufacturer should use to test the above null hypothesis?

b)The p-value of the hypothesis test is?

4.A company has found that the proportion of claims made on travel insurance policies of up to 30 days to Europe is 0.2421.It examines a sample of 250 policies and tries to find the probability that the proportion of claims made of these policies is more than 0.25

What Z value should it use to calculate this. probability? Four decimal places