1)A group of 110 students sat an aptitude test, their resultingscores are presented:

66
61
66
76
70
64
67
66
71
64
63
61
65
67
67
72
62
64
69
65
72
53
76
69
60
76
70
62
70
71
71
71
64
63
69
65
79
63
64
66
61
58
80
74
61
67
70
62
71
69
79
75
73
72
66
68
72
72
67
63
76
61
75
64
84
73
53
76
71
65
64
61
74
74
72
78
70
83
77
79
67
69
79
66
62
70
75
66
61
75
77
69
75
63
68
69
74
76
79
72
72
58
67
65
58
75
53
62
64
76

a)Calculate the mean and standard deviation for the sample. Giveyour answers to 2 decimal places.

sample mean = ?

sample standard deviation = ?

b)Find the proportion of scores that are within 1 standarddeviation of the sample mean and also the proportion that arewithin 2 standard deviations of the sample mean. Use the unroundedvalues for the mean and standard deviation when doing thiscalculation. 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)Select the appropriate description for the data:

a)the data are APPROXIMATELY normal
b)the data are CLEARLY not normal

d)Calculate the standardized value for the sample value 75. Notethat, for a value x within a sample that is approximatelydistributed as N(x,s), a standardized value can be calculated as z= (x - x) / s

standardized value (to 2 decimal places) for the sample value 75= ?

e)Calculate the probability that a standard normal randomvariable Z takes a values less than the standardized valuecalculated in part d). Give your answer as a decimal to 4 decimalplaces.

Probability Z less than standardized value = ?

f)Find the proportion of values in the sample that are less than75. Give you answer as a decimal to 2 decimal places.

Proportion of values less than 75 = ?

2)

A group of mutual funds earned varying annual rates of return inthe last year. These rates of return are normally distributed witha mean of 6% and a standard deviation of 17%.

One mutual fund in this group managed to earn a rate of returnthat was double that of this group's average that year. Thisperformance would put the fund in the top X% of those funds in thatyear.

Calculate X%. Give your answer to 1 decimal place.

X% = %