Answer:
So in range "-35.6108 to 39.73"; 50% data set can be found
ux = 37.6704 unites
Step-by-step explanation:
Step One: State the given parameters
From the question we are given that
mean Ц =2.06 unites
Standard deviation б is = 55.85 unites
Probability density → Normal
Let assume that it is symmetrically distributed about the mean
Step Two: Determine the range of the values
Our goal is to determine the range of values in which 50% of the data set should be found . Assuming that the range is from [tex]x_{1}[/tex] to [tex]x_{2}[/tex] and between these these we found 50% data set Hence from 0 up to [tex]x_{1}[/tex] we found 25% and up to [tex]x_{2}[/tex] we found 75% of the data set therefore z value corresponding to [tex]x_{1}[/tex] is - 0.6745 and the the z value corresponding to [tex]x_{2}[/tex] is +0.6745 (Refer to the z-table for normal distribution) as shown o the diagram on the first uploaded image
The formula for z is
z = [tex]\frac{x-mean}{standard deviation}[/tex]
for [tex]x_{1}[/tex] ,z = - 0.6745 ,substituting into the formula
[tex]-0.6745 = \frac{x_{1}-2.06}{55.85}[/tex]
=> -37.67 = [tex]x_{1}[/tex] -2.06
=> [tex]x_{1}[/tex] = -35.6108 unites
for [tex]x_{2}[/tex] , z = 0.6745 , substituting into the formula
[tex]0.6745 = \frac{x_{2}-2.06}{55.85}[/tex]
=> 37.67 = [tex]x_{2}[/tex] -2.06
=> [tex]x_{2}[/tex] = 39.73 units
So in range "-35.6108 to 39.73"; 50% data set can be found
ux = (39.73 - (-35.73) )/2
= 37.6704 unites
