Question

Given X = (43, 67, 34, 48, 52). What is the x value corresponding to z-score of ̴1.49 for this data set?

Answer 1

The value of X corresponding to z=1.49 is 270.63

The relation between x and z is given as

z=x-μ/σ

here μ is the mean and σ is standard deviation

The mean of the data set is calculated as

μ=(43+67+34+48+52)/5

=48.8

The standard deviation is calculated as

σ=((43-48.8)^2+(67-48.8)^2+(34-48.8)^2+(48-48.8)^2+(52-48.8)^2)/(5-1)

=148.7

Now the x value is calculated as

1.49=(x-48.8)/148.7

x=270.63