Question

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)

1. 160 and 200
2. 140 and 220
3. 120 and 240  
4. 100 and 260
5. 80 and 280  

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

Answer 1

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.