ANSWER:
(a) 95.44%
(b) 2.28%
(c) 15.87%
(d) 81.85%
Explanation:
Given:
μ = 66
σ = 4
We must calculate the value of z in each case depending on the values given, we calculate the value of z as follows:

(a) between 58 and 74.
P (58 < x < 74)
![\begin{gathered} P(58We determine these values with the table, just like this:<p>Therefore:</p>[tex]\begin{gathered} P(z<2)-P(z<-2)=0.9772-0.0228 \\ \\ P(58<p>(b) above 74</p><p>P (x > 74) </p>[tex]\begin{gathered} P(x>74)=1-P(x<74) \\ \\ P(x\gt74)=1-P\left(z<(74-66)/(4)\right) \\ \\ P(x\gt74)=1-P\left(z<2\right) \\ \\ P(x\gt74)=1-0.9772 \\ \\ P(x\gt74)=0.0228=2.28\% \end{gathered}]()
(c) below 62.
P (x < 62)

We determine this value with the table, like this:
Therefore:

(d) between 62 and 74.
P (62 < x < 74)
[tex]\begin{gathered} P(58