Question

In a survey by the National Association of Accountants, 60% of the corporate accountants who respondeddid not know what effect the law would have on their corporate liabilities. Suppose that this percentage applies to all corporate accounts, and n=19 corporate acconants are questioned reguarding the new tax law.

A. Find the probability that at least 15 of the 19 do not know what the effect the law will have on their corporate tax liabilities.

B. Find the probability that no more than 10 do not know what the effect the law will have.

Answer 1

X ~ Binomial(n , p) = Binomial(19,0.60)

Mean = np = 0.60 * 19 = 11.4

Standard deviation = np(1-p) = 19 * 0.60 * 0.40 = 2.1354

P( X < x) = P( Z < x - Mean / standard deviation)

A)

P( X >= 15) = P( X > 14.5) Using continuity correction

P( X > 14.5) = P (Z > 14.5 - 11.4 / 2.1354)

= P( Z > 1.4517)

= 1 - P( Z < 1.4517)

= 1 - 0.9267

= 0.0733

B)

P( X < 10) = P( X < 9.5) Using continuity correction

P( X < 9.5) = P( Z < 9.5 - 11.4 / 2.1354)

= P( Z < -0.8898)

= 1 - P( Z < 0.8898)

= 1 - 0.8132

= 0.1868