6. A population has a standard deviation of'4. What size sample should be taken to estimate the mean within two units ofthe true value with 95% probability? [4 marks} A researcher claims that Fijian families use an average of 18 coconuts per month with standard deviation of 3. Test the null hypothesis that He: ,u=18 against the alternative hypothesis that HA: ,u # 18 if a random sample of 100 Fijian families is found to consume an average of 20 coconuts per month. Use 6 % level of significance and state your conclusion clearly. (5 marks} Define: Type 11 error [2 marks) l. The following histogram shows the heights of students within a class: 20 g 16 C 4;} 12 '5 E s E 3 Z 4 125 130 135 140 145 150 155 160 Height (In cm) 1 a) How many students were surveyed? (2 marks) b) How many students have a height ofless than 140 cm? (2 marks) c) How many students have a height greater than 140 em but less than 155 cm? (2 marks) d) Calculate the probability that a student selected at random has height less than 140 cm. (2 marks) 2. A car trip uses a mean of 7 litres of petrol with a standard deviation of 0.5 litres. Assuming that the amount of petrol used is normally distributed a) What is the probability that the car trip uses between 6.7 and 13 litres on a trip? (3 marks) b) If the car usually takes only 8 litres of petrol in its tank, how many times in the next 1000 such trips will it run out of petrol? (4 marks} 3. A study of 49 Maths teachers showed that they spent, on average, 10.5 minutes correcting a student's exam paper with a standard deviation of 3.5 minutes. Find the 98.4% condence interval of the mean time for all exam papers. (4 marks)