1. If a set of data follows a normal curve distribution, with a mean of 180 and a standard deviation of 20, then approximately 95% % of the data lies in a region centered round the mean between values of (3 points)
2. Calculate by hand the range, variance and standard deviation for this data. Round your answers to two decimal points. (12 points)
20, 24, 26, 28, 30
1. Since the distribution is normal hence it follows empirical rule of standard deviation. as
So, within 2 standard deviation 95% of data lies so,
180-2*20= 140 and
180+2*20= 220
S0, within {140. 220} 95 5 0f data lies.
2. For the given data the mean is calculated as
and standard deviation is calculated as
s= 3.85
and Variance= s2 =3.852 =14.82
and Range= Maximum-Minimum
=30-20
=10.
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