Question

9.) Find the normal approximation for the binomial probability of P(x-3) where n 13 and p 60 (don't use binomial probability) 10)Find the normal approximation for the binomial probability of Pior-3) where n - 12 and p .5 (don't use binomial probability)

Given are the zscores

Show all work please

Answer 1

9) P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = np

Standard deviation = $\sqrt{npq}$

Given, n = 13, p = 0.6

q = 1 - p = 0.4

Mean = 13x0.6 = 7.8

Standard deviation = $\sqrt{13\times0.6\times0.4}$ = 1.766

P(X = 3) = P(2.5 < X < 3.5)

= P(X < 3.5) - P(X < 2.5)

= P(Z < (3.5 - 7.8)/1.766) - P(Z < (2.5 - 7.8)/1.766)

= P(Z < -2.43) - P(Z < -3.00)

= 0.0075 - 0.0013

= 0.0062

10) Given, n = 12, p = 0.5

Mean = 12x0.5 = 6

Standard deviation = $\sqrt{12\times0.5\times0.5}$ = 1.732

P(X = 3) = P(X < 3.5) - P(X < 2.5)

= P(Z < (3.5 - 6)/1.732) - P(Z < (2.5 - 6)/1.732)

= P(Z < -1.44) - P(Z < -2.02)

= 0.0749 - 0.0217

= 0.0532