Question

If X is a normal random variable with parameters µ = 10 and σ 2 = 36, compute

(a) P(X > 5),
(b) P(4 < X < 16),
(c) P(X < 8),
(d) P(X < 20),
(e) P(X > 16).

Answer 1

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 = $\frac{x-10}{6}$

is N(0,1)

a)  P(X > 5),

=$P(Z>-0.8333)\\=0.7977$

(b) P(4 < X < 16),

=$P(|z|<1)\\=0.6826$

(c) P(X < 8),

=$P(Z<-0.67)\\= 0.2525$

(d) P(X < 20),

=$P(Z<1.6667)\\= 0.9522$

(e) P(X > 16).

=P(Z>-0.6667)

= 0.2524