Question

A data set that X that is normally distributed with µ = 400 and a σ = 20.

    a.  What is P(370 < X < 410) = _________

    b. Determine the value of X such that 60% of the values are greater than that value. _____

PLEASE SHOW ALL YOUR WORK

Answer 1

solution

P(370< x <410 ) = P[(370-400) /20 < (x - ) / < (410-400) /20 )]

= P(-1.5 < Z <0.5 )

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

Using z table   

=0.6915-0.0668

probability= 0.6247

(B)

Using standard normal table,

P(Z > z) = 60%

= 1 - P(Z < z) = 0.60

= P(Z < z ) = 1 - 0.60

= P(Z < z ) = 0.40

= P(Z < - 0.25 ) = 0.40

z = - 0.25 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= -0.25*20+400

x= 395