Answer:
The notation for the uniform distribution is
X ~ U(a, b), where a = the lowest value and b = the highest value
In your case, X ~ U(66,89)
µ = (b+a)/2
Ď = (b-a)²/12
In this case, a = 66 and b = 89
Thus,
µ = (89+66)/2 = 77.5
Ď = (89-66)²/12 = 44.0833
Then, because we now know the true/population µ and Ď, we can use z-scores.
z = (X-µ)/Ď
In our case, X = 71. So,
Z = (X-µ)/Ď
Z = (71-77.5)/44.0833 = -0.15
P(Z>-0.15) = P(Z<0.15) = 0.5596
