Determine if the probability notation is adequate in each case when Z ∼ N(0, 1). For
a) X ∼ N(32.5, 6.3), the probability that the random variable is less than 37.48 is P(Z < 37.48).
b) X ∼ N(177, 9), the probability that the random variable is at least 164 is P(Z ≥ 164).
c) X ∼ N(12.25, 0.75), the probability that the random variable is greater than 11.90 is P(X > 11.90).
d) X ∼ N(1500,115), the probability that the random variable is no more than 1380 is P(Z ≤ −1.04).