1)a) P(61 < X < 64)
= P((61 - )/ < (X - )/ < (64 - )/)
= P((61 - 64)/2.9 < Z < (64 - 64)/2.9)
= P(-1.03 < Z < 0)
= P(Z < 0) - P(Z < -1.03)
= 0.5 - 0.1515
= 0.3485
b) P(57 < X < 71)
= P((57 - )/ < (X - )/ < (71 - )/)
= P((57 - 64)/2.9 < Z < (71 - 64)/2.9)
= P(-2.41 < Z < 2.41)
= P(Z < 2.41) - P(Z < -2.41)
= 0.9920 - 0.0080
= 0.9840
c) P(X < 71)
= P((X - )/ < (71 - )/)
= P(Z < (71 - 64)/2.9)
= P(Z < 2.41)
= 0.9920
d) P(X > 57)
= P((X - )/ > (57 - )/)
= P(Z > (57 - 64)/2.9)
= P(Z > -2.41)
= 1 - P(Z < -2.41)
= 1 - 0.0080
= 0.9920
e) P(X < 57) + P(X > 71)
= P((X - )/ < (57 - )/) + P((X - )/ > (71 - )/)
= P(Z < (57 - 64)/2.9) + P(Z > (71 - 64)/2.9)
= P(Z < -2.41) + P(Z > 2.41)
= P(Z < -2.41) + (1 - P(Z < 2.41))
= 0.0080 + (1 - 0.9920)
= 0.0080 + 0.0080 = 0.0160
2)a) P(X < h) = 0.25
or, P((X - )/ < (h - )/) = 0.25
or, P(Z < (h - 63)/2.6) = 0.25
or, (h - 63)/2.6 = -0.67
or, h = -0.67 * 2.6 + 63
or, h = 61.3
p = 25%
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