X has a normal distribution with the given mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
μ = 39, σ = 20, find
P(34 ≤ X ≤ 46)
Solution :
Given that ,
mean = = 39
standard deviation = =20
P(34 ≤ X ≤ 46) = P[(34-39) /20 < (x - ) / < (46-39) /20 )]
= P(-0.25 < Z <0.35 )
= P(Z <0.35 ) - P(Z < -0.25)
Using z table
= 0.6368 - 0.4013
probability= 0.2355
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