Problem 3. (15 points) 41 people were randomly selected and asked how many trips to the supermarket they had made in the past week. The responses are shown in the frequency table below. Calculate the sample mean and standard deviation of the data set. Number of supermarket trips Frequency 0 2 1 11 2 19 3 7 4 2 Total 41 Note: Round off your answer for the mean to 1 decimal places, and your answer for the standard deviation to 2 decimal. Do NOT round off intermediate calculations for finding the standard deviation. Mean = Standard deviation =Problem 5. (14 points) The mean time in a men's 400-meter dash is 47.78 seconds, with a standard deviation of 3.65 seconds. Apply Chebychev's Theorem to the data to find the interval that contains at least 75% of all times in the men's 400-meter dash. At least 75% of the times in the men's 400-meter dash are between sec and sec . Note: Use 2 decimal places in your answers. Note: You can earn partial credit on this problem.Problem 7. (15 points) In a survey of 193 people, the following data were obtained relating gender to political orientation: Republican (R) Democrat (D) Independent (1) Total Male (M) 53 34 31 118 Female (F) 32 24 19 75 Total 85 58 50 193 A person is randomly selected. What is the probability that the person is: a) Female? b) Female and a Republican? c) Female given that the person is a Republican? Note: Round your answers to 5 decimal places. Note: You can earn partial credit on this