Answer Happy

2. The body masses (in grams) of 151 Adelie penguins living in the Palmer Archipelago in Antarctica were recorded as part of the Palmer Station Long Term Ecological Research (LTER) Program | This data is stored in the Excel file called Adelie.xlsx, which can be downloaded from the LMS. The data consists of a single column with the heading "Body Mass". You are required to use Excel to answer the questions below. We will treat this data as population data for this question. (a) Calculate the population average of the penguin body masses provided in the Excel file. What is the population average and what was the Excel formula that you used to calculate it? (2 marks) (b) Calculate the population median of the penguin body masses provided in the Excel file. What is the population median and what was the Excel formula that you used to calculate it? (2 marks) (c) Calculate the population standard deviation of the penguin body masses provided in the Excel file. What is the population standard deviation and what was the Excel formula that you used to calculate it? (3 marks) (d) The empirical rule in statistics states that if the data in the population is approximately normally dis- tributed, then approximately 95% of the values in a population should fall within the interval u +20 (where u and o are the population average and population standard deviation respectively). (i) If the body masses of the Adelie penguins are approximately normally distributed, then how many of the 151 values would you expect to fall within the interval 4 20? Explain how you arrived at your answer. (1 mark) (ii) Use Excel to calculate how many of the 151 body masses in the data set fall within the interval u 20? Explain how you arrived at your answer. NOTE: there are several ways to do this. If you are not sure how then try searching the Internet. (2 marks)
(iii) What percentage of the 151 body masses fall within the interval u +20 (round to 2 decimal places)? (1 mark) (iv) Do you think there is evidence to suggest that the body masses of the Adelie penguins are approximately normally distributed? Explain. (2 marks)
1 2 3 4 5 6 7 8 Body Mass 3750 3800 3250 3450 3650 3625 4675 3475 4250 3300 3700 3200 3800 4400 9 10 11 12 13 14 15 16 3700 3450 17 18 4500 19 20 21 22 3325 4200 3400 3600 3800 3950 3800 3800 23 24 25 26 27 28 29 30 3550 3200 3150 3950 31 32 33 34 3250 3900 3300 3900 3325 4150 3950 3550 35 36 37 38
3550 38 39 40 3300 4650 41 3150 42 43 44 45 46 3900 3100 4400 3000 4600 3425 2975 3450 4150 3500 47 48 49 50 51 4300 52 53 54 55 3450 4050 2900 3700 56 57 3550 58 59 3800 2850 60 61 3750 3150 4400 3600 4050 62 63 64 65 66 67 68 69 2850 3950 3350 4100 3050 4450 3600 3900 3550 4150 70 71 72 73 74 75 76 77 78 3700 4250 3700 3900 3550 4000 79 80 81 82 83 84 3200 4700 3800 4200 3350 3550 3800 85 86 87 88 3500 89 90 3950 3600 3550 91
91 92 93 3550 4300 3400 4450 3300 4300 94 95 96 97 3700 98 4350 2900 99 100 101 102 103 104 105 106 107 108 109 4100 3725 4725 3075 4250 2925 3550 3750 3900 3175 4775 3825 110 4600 3200 111 112 113 114 115 116 117 118 119 4275 3900 4075 120 2900 3775 3350 3325 3150 3500 3450 3875 3050 4000 3275 4300 3050 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 4000 3325 3500 3500 4475 3425 3900 3175 3975 139 3400 140 141 142 143 4250 3400 3475 3050 144 3725
144 145 146 147 148 149 150 151 3725 3000 3650 4250 3475 3450 3750 3700 4000 152