Question

Suppose x has a distribution with μ = 53 and σ = 2.

Yes, the x distribution is normal with mean μ _x = 53 and σ _x = 0.5.

Find P(49 ≤ x ≤ 54).

Answer 1

Solution :

Given that ,

mean = = 53

standard deviation = = 2

= 53

=0.5

P(49 ≤ x ≤ 54) = P[(49-53) /0.5 < ( - ) / < (54-53) /0.5 )]

= P(-8 < Z <2 )

= P(Z <2 ) - P(Z <-8 )

Using z table

=0.9772-0

=0.9772

probability=  0.9772