statistics and probability

Question

Assume that � has a normal distribution with the specified mean and standard deviation.

Mean=6; standard deviation=1.1

Find the cutoff values of the middle 70%. Round your answers to 3 decimal places.

Low: x1=

High: X2

Answer 1

Because you're looking at the middle 70%, you should have 15% on both sides. You can find the corresponding z-score either in the table or in Excel using norm.inv(0.15,0,1) and norm.inv(0.85,0,1). Both methods will get you z-scores of ±1.04. So to find the x₁ and x₂ values, we simply add and subtract 1.04 standard deviations from the mean

6 ± 1.1•1.04 = 4.856 or 7.144

So our values are x₁=4.856 and x₂ = 7.144.

P.S. If you have Excel to work with for the whole problem, you can technically do the same norm.inv functions, but change the mean from 0 to 6 and standard deviation from 1 to 1.1.