Question 1: 22 points A social psychologist studying emotion presented a sample of 20 participants with pictures showing personal loss or tragedy and recorded the amount of time (in seconds) each participant spent looking at these pictures. Here is the data: 46, 33, 45, 110, 31, 35, 40, 39, 55, 52, 28, 16, 88, 74, 54, 44, 43, 52, 92, 23 a) Create a grouped frequency distribution using an interval width of 15. Include columns for cumulative frequency and cumulative percentage (4 marks). c) Complete the table below by entering the raw scores (from the beginning of question 1), the Deviation Scores, and the Squared Deviation Scores along with their sums. Use the table to calculate the mean, variance, and standard deviation using the definitional formulas (9 marks). (hint: you can use R to verify your calculations) X 0 0 4 d) Use the grouped frequency distribution from part (a) to interpolate the score associated with the first quartile (5 marks). You arrive at a pet store to purchase fish for your brand new aquarium. There are three types of fish: Swordtails, Bettas, and Dwarf Barbs. Moreover, some of the fish are red in colour while others are GOLD! You select your new fish using a fish- friendly net and wearing a blindfold so that each fish in the tank has an equal chance of being selected. The following table shows the frequency of the different fish in the tank: Gold Blue Red Swordtails 4 4 4 Bettas 1 5 6 Dwarf Barbs 2 6 9 a) What is the probability that you will draw a fish from the tank that is GOLD (3 marks)!? b) What is the probability that you will draw either a Swordtail or a blue fish from the tank (3 marks)? c) What is the probability that you will draw neither a Betta nor a red fish from the tank (3 marks)? d) What is the probability that your fish will be blue given that it is a Dwarf Barb (3 marks)? e) What is the probability that you and your friend will both draw GOLD fish without replacement (3 marks)?