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 70% of the values are greater than that value. _____

Answer 1

Solution :

Given that ,

mean = = 400

standard deviation = = 20

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) = 70%

= 1 - P(Z < z) = 0.70

= P(Z < z) = 1 - 0.70

= P(Z < z ) = 0.3

= P(Z < -0.52 ) = 0.3

z =-0.52

Using z-score formula,

x = z * +

x = -0.52* 20+400

x = 389.6

x=390 rounded