E| 2 of 9 1D: MST.CPD.ND.04.0030 [1 point] A teacher gives her class a particular examination on mathematics at the end of each year. The results are normally distributed with a mean test score of 57 and a standard deviation of B. The teacher has told the class that students with a test score in the top 2.5% will win a special prize. Calculate the test score above which 2.5% of all test scores lie. Give your answer to 1 decimal place. Test score = El 3 of 9 m: MST.CPD.ND.09.0010b [3 points] The heights, in inches, for 120 people (male and female) have been measured. The results are presented: Download the data 69.27 69.91 63.64 65.41 65.06 62.42 64.54 61.65 69.96 66.85 71.24 69.1 67.09 66.35 68.17 68.73 67.46 68.61 66.51 62.31 71.31 63.68 65.87 71.94 70.95 63.53 68.79 62.56 62.93 68.41 64.09 69.2 68.26 68.92 64.63 67 70.52 65.57 66.65 66.65 68.57 67.74 61.49 63.58 67.73 62.45 63.69 69.71 70.55 68.96 66.63 64.12 69.81 65.27 66.18 68.56 62.38 64.47 70.54 69.48 63.37 64.98 66.35 67.11 65.82 61.33 67.99 67.16 64.64 68.19 68.44 69.74 68.44 70.34 65.56 68.46 65.86 65.6 63.22 65.3 71.48 65.86 67.86 66.85 65.67 71.31 64.61 64.11 65.17 69.18 70.58 62.58 64.87 63.07 66.2 67.5 69.7 66.2 71.09 70.76 66.56 67.66 67.16 62.71 67.43 62.63 68.52 68.27 65.59 63.85 a) Calculate the mean and standard deviation for the sample. Give your answers to 2 decimal places. sample mean = sample standard deviation = b) Find the proportion of heights that are within 1 standard deviation of the sample mean and also the proportion that are within 2 standard deviations of the sample mean. Use the unrounded values for the mean and standard deviation when doing this calculation. Give your answers as decimals to 2 decimal places. Proportion of heights within 1 standard deviation of the mean = Proportion of heights within 2 standard deviations of the mean = c) Select the appropriate description for the data: the data are APPROXIMATELY normal the data are CLEARLY not normal 3) Calculate the mean and standard deviation for the sample. Give your answers to 2 decimal places. sample mean = sample standard deviation = h) Find the proportion of heights that are within 1 standard deviation of the sample mean and also the proportion that are within 2 standard deviations of the sample mean. Use the unraunded values for the mean and standard deviation when doing this calculation. Give your answers as decimals to 2 decimal places. Proportion of heights within 1 standard deviation of the mean = Proportion of heights within 2 standard deviations of the mean = c) Select the appropriate description for the data: the data are APPROXIMATELV normal the data are CLEARLY not normal d) Calculate the standardized value for the value 68, Note that, for a value x within a sample that is approximately distributed as N(;,s), a standardized value can be calculated as z = (x - x) / s standardized value (to 2 decimal places) for the value 68 = e) Calculate the probability that a standard normal random variable Z takes a values less than the standardized value calculated in part d). Give your answer as a decimal to 4 decimal places. Probability 2 less than standardized value = f) Find the proportion of values in the sample that are less than or equal to 68. Give you answer as a decimal to 2 decimal places, Proportion of values less than or equal to 68 = Gravel Road High School has two mathematics classes for each year. One class is a standard class containing students who possess standard mathematical ability. The other class is an advanced class containing the all-round brightest students in each year. Due to time tabling issues at the school, the studenls in the advanced class are selected based on their abilities in both English and mathematics (thus forming two advanced classes in one). The grades obtained by students in the standard mathematics class range from very low to very high. Most students gain marks between 60% and 70%, with an average mark of 65%. On rare occasions a student may severely fail, in which case this student is kept back a year: On similarly rare occasions a student may obtain a mark of over 90%, in which case this student is moved up to the advanced class. The grades obtained by students in the advanced class vary substantially between those students who are in the class because of their mathematical ability and those who are in the class because of their English ability. Most of the mathematically inclined students gain marks between 90% and 100%, with an average of 95%. Most of the students who are talented at English gain marks between 50% and 60%, with an average of 55%. Out of the standard and advanced classes, it would be more reasonable to model the grades of the a mathematics class with a normal distribution. 5 of 9 ID: MST.NDM.MPD.04.0010 3 oints