Question

Suppose X is a normal random variable with mean

μ = 70

and standard deviation σ = 5. Find a such that

P(X ≥ a) = 0.01.

(Round your answer to one decimal place.)

a =

Answer 1

Solution:-

Given that,

mean = = 70

standard deviation = = 5

Using standard normal table,

P(X ≥ a) = 0.01.

= 1 - P(Z < z) = 0.01  

= P(Z < z) = 1 - 0.01

= P(Z < z ) = 0.99.  

z =2.33 ( using z table )

Using z-score formula,

x = z * +

=2.33*5+70

x=81.6

a=x=81.6