Question

If X is normally distributed with mean 30 and standard deviation 5. Find
(i) P26  X  40
(ii) PX  45
(iii) P X  30  5

Answer 1

Step-by-step explanation:

Given X ~ N (µ, σ ) µ = 30, σ = 4

(a) P(X < 40) = P(Z < (40 - 30)/4)

= P(Z < 2.5)

= 0.5 + P(0 < Z < 2.5)

= 0.5 + 0.4938

= 0.9938

(b) P(X > 21) = P(Z > (21 - 30)/4)

= P (Z > -2.25)

= 0.5 + P(-2.25 < Z < 0)

= 0 5 + P (0 < Z < 2.25)

= 0.5 + 0.4878

= 0.9878

(c) P(30 < X < 35)

= P((30 - 30)/4 < Z < (35 - 30)/4)

= P(0 < Z < 1.25)

= 0.3944

Answer 2

Answer:

0.9355

Step-by-step explanation:

hope you understand