Question

66% of all Americans are homeowners. If 39 Americans are randomly selected, find the probability that:

C. At least 27 of them are homeowners. How to type this and get the answeron a calculator TI-83 plus.

Answer 1

Using Normal Approximation to Binomial
Mean = n * P = ( 39 * 0.66 ) = 25.74
Variance = n * P * Q = ( 39 * 0.66 * 0.34 ) = 8.7516
Standard deviation = √(variance) = √(8.7516) = 2.9583

Condition check for Normal Approximation to Binomial
n * P >= 10 = 39 * 0.66 = 25.74
n * (1 - P ) >= 10 = 39 * ( 1 - 0.66 ) = 13.26

P ( X >= 27 )
Using continuity correction
P ( X > n - 0.5 ) = P ( X > 27 - 0.5 ) =P ( X > 26.5 )

Press 2ND + Vars

P ( X > 26.5 ) = 0.3986