Question

Let X be normally distributed with mean μ = 4.1 and standard deviation σ = 3.

b. Find P(5.5 ≤ X ≤ 7.5).

c. Find x such that P(X > x) = 0.0485.

Answer 1

Solution :

Given that ,

mean = = 4.1

standard deviation = = 3

P( 5.5  x 7.5)

= P[( 5.5 -4.1 /3 ) (x - ) / ( 7.5 -4.1/ )3 ]

= P( 0.47 z 1.13)

= P(z 1.13) - P(z 0.47)

Using z table,   

=  0.8708 -0.6808

probability=0.1900

(c)  

Using standard normal table,

P(Z > z) =0.0485

= 1 - P(Z < z) = 0.0485

= P(Z < z ) = 1 - 0.0485

= P(Z < z ) = 0.9515

= P(Z < 1.66) = 0.9515  

z = 1.66 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x=1.66 *3+4.1

x= 9.08

x=9