Mean = n = 40 * 0.4 = 16
Standard deviation = sqrt [ n ( 1 - ) ]
= sqrt [ 40 * 0.4 * 0.6]
= 3.0984
Using normal approximation,
P(X < x) = P(Z < x - Mean / SD)
a)
P(X = 25) = P(24.5 < X < 25.5) [ With continuity correction ]
= P(X < 25.5) - P(X < 24.5)
= P(Z < (25.5 - 16) / 3.0984 ) - P(Z < (24.5 - 16) / 3.0984 )
= P(Z < 3.07) - P(Z < 2.74)
= 0.9989 - 0.9969
= 0.0020
b)
P(X > 25) = P(Z > (25.5 - 16) / 3.0984)
= P(Z > 3.07)
= 0.0011
c)
P(X <= 25) = P(Z < (25.5 - 16) / 3.0984)
= P(Z < 3.07)
= 0.9989
d)
P(X < 25) = P(Z < (24.5 - 16) / 3.0894)
= P(Z < 2.74)
= 0.9969
For n = 40 and 1 = 0.4, use the normal distribution to approximate the following...
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