Sahil Khan
0

We find the z-score for 48 dollars and 60.5  dollars


z_{1} = \frac{x_{1}-\mu}{\sigma}

Substituting x_{1} = 48, \mu = 58, and \sigma = 5

z_{1} = \frac{48 - 58}{5} = -2  

Substituting x_{2} = 60.5, \mu = 58, and \sigma = 5

z_{2} = \frac{x_{2}-\mu}{\sigma}

z_{2} = \frac{60.5-58}{5} = 0.5


Looking up z_{1} = -2 in the z-score table we get 0.0228 of sweater prices are below 48 dollars.

Similarly looking up z_{2} = 0.5 in the z-score table we get  0.6915 of sweater prices are below 60.5 dollars.


To find the area between z_{1} and z_{2} we get z_{2} - z_{1} = 0.6915 - 0.0228 = 0.6687.

So, 0.6687 proportion of sweater prices lie between 48 dollars and 60.5 dollars.