Answer:
Step-by-step explanation:
Given that X is a normal random variable with parameters µ = 10 and σ 2 = 36,
X is N(10, 6)
Or z = [tex]\frac{x-10}{6}[/tex]
is N(0,1)
a) P(X > 5),
=[tex]P(Z>-0.8333)\\=0.7977[/tex]
(b) P(4 < X < 16),
=[tex]P(|z|<1)\\=0.6826[/tex]
(c) P(X < 8),
=[tex]P(Z<-0.67)\\= 0.2525[/tex]
(d) P(X < 20),
=[tex]P(Z<1.6667)\\= 0.9522[/tex]
(e) P(X > 16).
=P(Z>-0.6667)
= 0.2524
