Find the probability that x is between five and 11. X ~ N(6, 3)

Expert Solution

the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 6
standard Deviation ( sd )= 3
To find P(a < = Z < = b) = F(b) - F(a)
P(5 < X < 11) = P(X < 11) - P(X < 5)

= P(x - u / sd<(11-6)/3) - P(x - u / sd<(5-6)/3)

= P ( Z <1.67) - P ( Z <-0.33)

=0.9522 - 0.3707

There fore P(5 < X < 12) = 0.5815

orchestra answered 1 year ago

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