Find P(X>6) if the mean is 22 and the standard deviation is 16

Question

Find P(2≤X≤26)

Find P(10≤X≤30)

Answer 1

P(x > 6)

x is N(22,6)

To find probability convert inequality using x to using N(0,1) z variable: (x - mean)/standard deviation

P(z > (6-22)/16)

P(z > -1 ) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413

P(2 <= x <= 26)

convert inequality using x to using N(0,1) z variable

P( (2-22)/16 <= z <= (26-22)/16) = P(-1.25 < z < 0.25) = P(z <= 0.25) - P(z <= -1.25) = 0.5987 - 0.1056 = 0.4931

P(10 <= x <= 30)

convert inequality using x to using N(0,1) z variable

P( (10-22)/16 <= z <= (30-22)/16) = P(-0.75 <= z <= 0.5) = P(z <= 0.5) - P(z <= -0.75) = 0.6915 - 0.2266 = 0.4649