Question 1 |24 marksl a) State whether the following is a discrete or continuous random variable. Number of seeds in a tomato [1] The number of litres of water used per household [l] iii. The ages ofchildren in a preschool [I] b) Determine the sampling methods used In each of the scenarios below i. ii. iii. iv. Select every 9* candy bar from a production line to check its weight [I] Group t- shirts by colors and select t- shirts at random from within each group in proportion to the number of t-shirts that make up that group. [I] Use random number tables to select 15 students from a class. [1] Select 8 white cars, 5 blue and 3 red cars. [I] Name one advantage of the sampling method in ii) [I] c) The following stem-and leaf display shows the weight, in kilogram, boxes of juice Stem-and-Leaf Display N = Leaf Unit = 0.1 9 0 002334666 20 1 01123356777 (**) 2 00122223346799 * * * 3 56778899 12 4 0002344 5 5 66789 i. Determine the values of * ** and *** i1. What is the value of the median? 3ZEW 111. Find the modal yield of this data set. iv. What is the range of the data set?d) The weight of 45 watermelons from a farm is shown below. Weight Frequency 11-15 16-20 8 21-25 13 26-30 11 31-35 9 Calculate the mean [2] ii. Calculate the median [3] Calculate the mode [3] iv . Comment on the skewness of this distribution. [2]Question 2 [15 marks] a) In a pastry shop in a small town, the probability that a customer buys apple tarts is 0.45, the probability they buy an apple pie is 0.69 and the probability that they buy both an apple tart and an apple pie is 0.27. A customer is chosen at random. i. Find the probability that they buy an apple tart or an apple pie. [3] ii. Given that a customer buys an apple pie, what is the probability that they also buy an apple tart? [3] b) The weight of a green forest frog has a normal distribution with mean 150.3 g and a standard deviation of 5g. Find the probability that a randomly selected frog weighs Less than 153g [2] ii. Between 150 g and 158 g [3] c) The random variable X is normally distributed such that X~N(#, 12). It is known that P(X > 32) = 0.0618. find the value of u. [4]Question 3 [16 marks] a) People who diet can expect to lose an average of 3kg in a month. In a book, the authors claim that people who follow a new diet will lose an average of less than 3kg in a month. The weight losses of the 180 people in a random sample who had followed the new diet for a month were noted. The mean was 2.7 kg and the standard deviation was 2.8kg. ECON1005 Introductory Statistics Semester 1 2022/23 Test the authors' claim at the 5% significance level, stating your null and alternative hypotheses. [6]b) From a sample of 200 bread rolls from Ideal bakery, 95 of the were wheat. The manager of the bakery claims that 49% of their rolls are wheat. i. Test at the 1% significance level to determine whether the true proportion is less than 49%. [6] ii. Create a 99% confidence interval for the proportion of all wheat bread rolls produced from Ideal bakery. [4]