Question 3 [l] The boxplot below is made from 100 teenagers of their sleep hours per day. Based on the plot, nd (L) mean 8L median (ii) interquartile (iii) range (iv) number of outliers. I Sleep Hours, Teens 13.00 16.00 '16.67 H.113 14.00 12.01] 11. '5 0.18 moo A2 son 25 son 5.49 -4.57 4.0!] 2.0!] [1.0!] [2] The mean and standard deviation of the wages of 600 factory workers are $41,000 and $3,300 respectively. If the wages have a mound (bell)-shaped distribution, how many workers are expected roughly to receive wages of between $37,700 and $44,300? Show your work. [3] A custom jobber of speciality breglass-bodied cars wished to estimate overhead expenses (labelled A and measured in $'000s) as a function of the number of cars (labelled B) produced monthly. A random sample of 10 months was recorded, and the following statistics were calculated: sample covariance ofA and B (100), sample variance ofA (10), sample variance ofB (250)= sample mean ofA (5), and sample mean of B (10). Compute the least squares regression line. Show your work. [4] Every year, dozens of new vaccines are developed. It is the responsibility of the Therapeutic Goods Administration (TGA) in Australia to judge the safety and eectiveness of the vaccines before approving them to be used for the public. The null and alternative hypotheses are as follows: Hg: The vaccine i unsafe and ineffective and HA: The Wine is safe and effective. Oen, TGA makes a__(_l_ _ogl based on data from animal experiments and human trials. Describe the two types of errors that TCA might commit. Now, suppose that a trial test result is with the pvalue equal to 0.015. What is the minimum signicance level that the null hypothesis can be rejected? Explain. [5] The amount of time that professional sport players devote to their trainings per day is normally distributed, with a mean of 6 hours and a standard deviation of 2 hours. Find the probability that the mean amount of training time per day for 16 randomly selected sport players is more than 7.5 hours. Show your work