which z - values correspond to the middle 10% of the standard normal distribution? round your answers to the…

Answer:

$- 0.126<z<0.126$

Explanation:

Step1: Determine the area in the tails

The middle area is 0.10. So the total area in the two - tails is $1 - 0.10=0.90$. The area in each tail is $\frac{0.90}{2}=0.45$.

Step2: Find the z - value for the left - tail

We want to find the $z$ - value such that the area to the left of it is $0.45$. Looking up in the standard normal table (or using a calculator with a normal - distribution function), the $z$ - value corresponding to an area of 0.45 is approximately $z=- 0.126$.

Step3: Find the z - value for the right - tail

Due to the symmetry of the standard normal distribution, the $z$ - value for the right - hand side of the middle 10% region has the same magnitude but opposite sign. So the right $z$ - value is $z = 0.126$.