Question 3:

Confidence Interval

i. List three strategies used to reduce the width of a confidence interval to make your estimate more precise. [ 2 marks]

ii. A researcher is designing a study to standardise a new intelligence test. It is known that scores on this type of test are normally distributed with a standard deviation of 15.0.

(a) Write down in terms of the sample mean, and n, the sample size, an expression for a 99% symmetric confidence interval for the mean test score. [ 3 marks]

(b) Calculate, to the nearest hundred, the value of n such that the width of this confidence interval will be less than 1.0. [ 3 marks]

Question 4:

Binomial and Poisson Distribution

a. Some students do no revision, so they always must guess the answers in multiple-choice examinations. There are 10 questions, each with 5 possible answers. The students need at least 7 correct answers to pass the test. Find the probability that the students pass. [4 marks]

On average a hardware store receives requests to hire out two truck drivers a day. Find the probability that on a given day there are at most two requests for truck drivers. [4 marks]

purple blue