Question

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

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

(A)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 ) = 0.30

= P(Z < - 0.52 ) = 0.30  

z = - 0.52 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x=- 0.52 *20+400

x= 389.6

x=390