Question

For of a bell-shaped data with mean of 100 and standard deviation of 16, approximately

a)0.15% of the values lies below __________

b)68% of the middle values lies between: _____________

c)2.5% of the values lies above: ____________

d)0.15% of the values lies above: ____________

Answer 1

Solution:

Given: a bell-shaped data is with mean of 100 and standard deviation of 16.

That is: and

Since data is bell shaped , we need to use Empirical rule to find x values for given percentage values.

Empirical rule is:

1) 68% of the data falls within 1 standard deviation from mean

2) 95% of the data falls within 2 standard deviation from mean

3) 99.7% of the data falls within 3 standard deviation from mean

.

Part a) 0.15% of the values lies below____?

Since 99.7% values are within 3 standard deviation from mean, then 100-99.7=0.30% values are outside the 3 standard deviation from mean.

Thus 0.30/2=0.15% values are below 3 standard deviation from mean and remaining 0.15% values are above 3 standard deviation from mean.

Thus find:

Thus 0.15% of the values are below 52.

Part b) 68% of the middle values lies between:______?

According to Empirical rule 68% of the data falls within 1 standard deviation from mean

Thus find:

  

and

Thus 68% of the middle values lies between 84 and 116

Part c) 2.5% of the values lies above:____?

According to Empirical rule 95% of the data falls within 2 standard deviation from mean

then 100 - 95 = 5% of values fall outside the 2 standard deviation from mean.

That is: 5%/2=2.5% of values fall below the 2 standard deviation from mean and remaining 2.5% of values fall above the 2 standard deviation from mean.

Since we have to find 2.5% of the values lies above, find:

Thus 2.5% of the values lies above 132.

Part d) 0.15% of the values lies above:_______?

Since 99.7% values are within 3 standard deviation from mean, then 100-99.7=0.30% values are outside the 3 standard deviation from mean.

Thus 0.30/2=0.15% values are below 3 standard deviation from mean and remaining 0.15% values are above 3 standard deviation from mean.

Thus find:

Thus 0.15% of the values are above 148.