The dimensions of Noah's ark according to the Bible had a length of 300 cubits, a breadth of 50 cubits, and a height of 30 cubits. While these values are believed to be exact, the size of a cubit varies anywhere between 457mm and 531mm in ancient cultures. Supposing that to the nearest millimetre a cubit is 495mm, find the volume of Noah's ark in cubic metres to the appropriate number of significant figures. Question 2 [1+2+2+2+2+1 = 10 marks] The following marks were obtained by the 11 students enrolled last semester in the unit "Essential Life Skills": 75, 99, 44, 80, 62, 87, 93, 72, 57, 90, 86. (a) For statistical questions pertaining to this particular class, is this population or sample data? (b) Find the mean mark obtained by the class. (e) Find the standard deviation for the marks data. (d) Draw an appropriate stem and leaf display for this data. (e) What is the median mark? (f) Is the data symmetrically distributed? If not, comment on the shape of the distribution. Question 3 [(2+2+1+1)+(2+3)= 11 marks] A research team is working hard to understand coronavirus (COVID-19) to better fight it. (a) The team is interested in knowing if there is a seasonal factor contributing to the contraction of the virus. They access and randomly select the data from 350 people around the world and determine in what season they contracted the virus. i) State appropriate null and alternate hypotheses that the team would use in an attempt to get statistical evidence that there are seasonal variations to catching the virus. ii) The seasons in which patients contracted the virus was as follows: Autumn Winter Spring Summer 96 69 80 105 Determine the value of the x2 test statistic. iii) Given that the Excel command -CHIINV (0.05,3) returns the value of 7.8147, at the a=0.05 level of significance, determine if the null hypothesis is rejected or not. iv) State what conclusion can be made from this hypothesis test. (b) The team has found that the recovery time from the COVID-19 virus is normally distributed with a mean of 17 days and a standard deviation of 8 days. i) Given that the Excel command -NORMDIST (21,17,8,TRUE) returns the value 0.691, what percentage of virus victims take more than 21 days to recover? ii) What percentage those infected by the virus take between 9 and 21 days to recover?