The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is between 14.3 and 16.1.
Solution :
Given that ,
mean = = 15.2
standard deviation = = 0.9
P(14.3< x < 16.1) = P[(14.3-15.2) / 0.9< (x - ) / < (16.1-15.2) /0.9 )]
= P(-1 < Z < 1)
= P(Z <1 ) - P(Z <-1 )
Using z table
= 0.8413-0.1587
probability= 0.6826
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