Mean = np = 52 * 0.15 = 7.8
Standard deviation = sqrt ( n p( 1 - p) )
= sqrt ( 52 * 0.15 * 0.85)
= 2.5749
Using normal approximation,
P(X < x) = P(Z < x - Mean / SD)
a)
P(X > 8) = P(Z > 8.5 - 7.8 / 2.5749) , Using continuity correction
= P(X > 0.27)
= 0.3936
b)
P(X >= 8) = P(Z > 7.5 - 7.8 / 2.5749) , Using continuity correction
= P( Z > -0.12)
= P( Z < 0.12)
= 0.5478
c)
P(X = 8) = P(7.5 < X < 8.5) , Using continuity correction,
= P(X < 8.5) - P(X < 7.5)
= P(Z < (8.5 - 7.8) / 2.5749) - P(Z < (7.5 - 7.8) / 2.5749)
= P(Z < 0.27) - P(Z < -0.12)
= 0.6064 - 0.4522
= 0.1542
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