Question

Given that x is a normal variable with mean μ = 48 and standard deviation σ = 6.2, find the following probabilities. (Round your answers to four decimal places.)

(a)  P(x ≤ 60)


(b)  P(x ≥ 50)


(c)  P(50 ≤ x ≤ 60)

Answer 1

Solution :

Given that,

mean = = 48

standard deviation = = 6.2

P(x ≤ 60)= P[(X- ) / < (60-48) / 6.2]

= P(z <1.94 )

Using z table

probability= 0.9738

b.

P(x ≥ 50) =1 - P[(X- ) / < (50-48) / 6.2]

=1 - P(z <0.32 )

Using z table

= 1 -0.6255

probability=0.3745

c.

P(50 ≤ x ≤ 60) = P[ (50-48) / 6.2< (x - ) / < (60-48) / 6.2]

= P( 0.32< Z <1.94 )

= P(Z <1.94 ) - P(Z <0.32 )

Using z table   

= 0.9738-0.6255

probability= 0.3488

answered by: anonymous