A group of 110 students sat an aptitude test, their resulting scores are presented: 55 64 74 74 53 67 73 71 Scores: 72 62 65 66 59 72 66 83 76 59 70 60 62 66 66 68 66 73 63 67 67 58 69 68 69 61 76 60 70 70 77 73 65 70 66 67 78 71 64 70 73 57 80 74 70 69 63 61 67 61 61 65 65 73 77 69 77 73 68 64 76 62 61 65 73 82 66 64 63 60 72 78 74 a) Calculate the mean and standard deviation for the sample. Give your answers to 2 decimal places. 68 63 71 sample mean = 61 66 sample standard deviation = 66 80 Download the data b) Find the proportion of scores that are within 1 standard deviation of the sample mean and also the proportion that are within 2 standard deviations of the sample c) Select the appropriate description for the data: mean. Use the unrounded va Proportion of scores within 1 standard deviation of the mean = Proportion of scores within 2 standard deviations of the mean = Othe data are APPROXIMATELY normal Othe data are CLEARLY not normal ues for the mean and standard deviation when doing this calculation. Give your answers as decimals to 2 decimal places. (I) Calculate the standardized value for the sample value 70. Note that, for a value x within a sample that is approximately distributed as N(,s), a standardized value can be calculated as 2 = (x - x) / s standardized value (to 2 decimal places) for the sample value 70 = e) Calculate the probability that a standard normal random variable 2 takes a values less than the standardized value calculated in part cl). Give your answer as a decimal to 4 decimal places