They will require between 18.42 and 31.58 minutes.
We want the middle 90%. The two probability values associated with this would be 0.95 and 0.05; this would leave 5% below and 5% above, giving us the middle 90%.
Using a z-table (http://www.z-table.com) we see that the z-score associated with an area to the left of 0.05 is between -1.64 and -1.65; since it is equally distant from both we will use -1.645.
The z-score associated with an area of the left of 0.95 is between 1.64 and 1.65; since it is equally distant from both we will use 1.645.
The formula for a z-score is
z = (X-μ)/σ -1.645 = (X-25)/4
Multiplying by 4 on both sides, -1.645(4) = X-25 -6.58 = X-25
Adding 25 to both sides, -6.58+25 = X 18.42 = X
For the upper bound, 1.645 = (X-25)/4
Multiplying both sides by 4, 1.645(4) = X-25 6.58 = X-25
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