Question

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

μ = 4; σ = 6

P(1 ≤ x ≤ 13) =

Answer 1

Solution :

Given that ,

mean = = 4

standard deviation = = 6

P(1 ≤ x ≤ 13)

= P[( 1 - 4 / 6 ) (x - ) / ( 13 - 4 / 6 ) ]

= P( - 0.5   z 1.5 )

= P(z 1.5 ) - P(z - 0.5  )

Using z table,

= 0.9332 - 0.3085

= 0.6247

P(1 ≤ x ≤ 13) = 0.6247