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 = 8; σ = 2

P(7 ≤ x ≤ 11) =

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 = 20; σ = 3.4

P(x ≥ 30) =

Answer 1

Solution :

Given that ,

mean =   = 8

standard deviation = = 2

(A)P(7 ≤ x ≤ 11) = P[(7-8) /2 < (x - ) / < (11-8) /2 )]

= P( -0.5< Z <1.5 )

= P(Z <1.5 ) - P(Z <-0.5 )

Using z table   

= 0.9332-0.3085

probability= 0.6247

(B)Solution :

Given ,

mean = = 20

standard deviation = = 3.4

P(x ≥ 30 ) = 1 - P(x<30 )

= 1 - P[ X - / / (30-20) /3.4 ]

= 1 - P(z <2.94 )

Using z table

= 1 - 0.9984

= 0.0016

probability= 0.0016