Let X represent a binomial random variable with n = 360 and p = 0.82. Find the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.

Mean = np = 360 * 0.82 = 295.2
Standard deviation = sqrt (np(1p))
= sqrt (360 * 0.82 ( 1  0.82) )
= 7.2894
a)
P(X <= 290) = P(Z < (290.5  295.2) / 7.2894) (With continuity correction)
= P(Z < 0.64)
= 0.2611 (From Z table)
b)
P(X > 300) = P(Z < (300.5  295.2) / 7.2894) (With continuity correction)
= P(Z < 0.73)
= 0.2327 (From Z table)
c)
P(295 <= X <= 305) = P(294.5 < X < 305.5)
= P(Z < (305.5  295.2) / 7.2894)  P(Z < (294.5  295.2) / 7.2894) (With continuity correction)
= P(Z < 1.41)  P(Z < 0.10)
= 0.9207  0.4602 (From Z table)
= 0.4605
d)
P(X = 280) = P(279.5 < X < 280.5)
= P(Z < (280.5  295.2) / 7.2894)  P(Z < (279.5  295.2) / 7.2894) (With continuity correction)
= P(Z < 2.02)  P(Z < 2.15)
= 0.0217  0.0158 (From Z table)
= 0.0059
Get Answers For Free
Most questions answered within 1 hours.