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 = 22; σ = 3.4

P(x ≥ 30) =    

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 = 2

P(3 ≤ x ≤ 6) =

Answer 1

1)

Solution :

Given that ,

mean = = 22

standard deviation = = 3.4

P(x 30) = 1 - P(x   30)

= 1 - P((x - ) / (30 - 22) / 3.4)

= 1 -  P(z 2.35)  

= 1 - 0.9906 Using standard normal table.   

= 0.0094

Probability = 0.0094

2)

Solution :

Given that ,

mean = = 4

standard deviation = = 2

P( 3 x 6) = P(( (3 - 4 )/ 2) (x - ) / (6 - 4) / 2) )

P( 3 x 6) = P(-0.5 z 1)

P( 3 x 6) = P(z 1) - P(z -0.5)

P( 3 x 6) = 0.8413 - 0.3085 Using standard normal table.

Probability = 0.5328