55, 57, 57, 73, 63, 65, 60, 71, 58, 71, 62, 82, 63, 74, 69, 59, 64, 63, 76, 77,

Question

55,
57,
57,
73,
63,
65,
60,
71,
58,
71,
62,
82,
63,
74,
69,
59,
64,
63,
76,
77,
58,
77,
69,
75,
69,
70,
68,
63,
72,
63,
61,
73,
73,
83,
46,
62,
68,
67,
69,
60,
64,
64,
63,
77,
67,
77,
72,
74,
64,
71,
75,
70,
60,
63,
76,
64,
61,
68,
79,
77,
72,
55,
62,
59,
60,
77,
63,
64,
66,
79,
73,
61,
65,
75,
71,
72,
75,
64,
76,
67,
63,
69,
65,
79,
68,
79,
60,
69,
84,
69,
69,
66,
68,
80,
64,
65,
65,
74,
67,
67,
66,
77,
61,
62,
62,
70,
73,
66,
74,
64

9 of 20 ID: MST.CPD.ND.09.0010c.abe [5 points] A group of 110 students sat an aptitude test, their resulting scores are presented: Scores: 55 57 57 73 63 65 60 7158 71 62 82 63 7469 59 64 63 76 77 58 7769 75 69 70 68 63 72 63 61 73 73 83 46 62 68 67 69 60 64 64 63 77 6777 72 74 64 71 75 70 60 63 76 6461 6879 77 72 55 62 59 60 7763 64 66 79 73 61 65 75 71 72 7 63 69 65 79 68 79 60 69 84 69 69 66 68 80 64 6565 74 67 67 66 77 61 62 62 70 73 66 74| 64 75 64 76 67 a) Calculate the mean and standard deviation for the sample. Give your answers to 2 decimal places sample mean 68.05 sample standard deviation = 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 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 scores within 1 standard deviation of the mean Proportion of scores within 2 standard deviations of the mean c) Find the proportion of values in the sample that are less than 65. Give you answer as a decimal to 2 decimal places Proportion of values less than 65 =

Explanation / Answer

A)

B)FOR A NORMAL DISTRIBUTION BY 68-96-99.7 RULE THE 68% ARE UNDER ONE STANDARD DEVIATION AND 95% ARE UNDER TWO STANDARD DEVIATION

= THEREFORE FOR 68% = 0.68

Z SCORE = 0.47

HENCE X = MEAN+Z*STANDARD DEV = 67.92+0.47*6.91=71.16

FOR 95% = 0.95

THE Z SCORE = 1.65

X = 67.92+1.65*6.91 = 79.32

C)P(X<65)

For x = 65, the z-value z = (65 - 67.92) / 6.91 = -0.42   

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