Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 14.6; σ = 3.2

P(8 ≤ x ≤ 12) =

Answer 1

Solution :

Given that ,

mean = = 14.6

standard deviation = = 3.2

P(8 x 12) = P(( 8 - 14.6 / 3.2) (x - ) / (12 - 14.6 / 3.2) )

= P(-2.0625 z -0.8125)

= P(z -0.8125) - P(z -2.0625)

= 0.2083 - 0.0196

= 0.1887

P(8 x 12) = 0.1887

Probability = 0.1887