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).
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
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