Question

Suppose that 25% of all home buyers will do some remodeling to their home within the first five years of home ownership. Assuming this is true, use the binomial distribution to determine the probability that in a random sample of 15 homeowners, or fewer will remodel their homes. The probability that 2 or fewer people in the sample indicate that they will remodel their homes is [ans 1]. (Round to four decimal places as needed.)

Answer 1

solution:-

given that p = 0.25 , n = 15

formula

=> P(X = x) = ncx * p^x * (1-p)^(n-x)

=> P(X = 2 or fewer) = P(x = 0) + P(x = 1) + P(x = 2)

= 15c0 * 0.25^0 * (1-0.25)^(15-0) + 15c1 * 0.25^1 * (1-0.25)^(15-1) + 15c2 * 0.25^2 * (1-0.25)^(15-2)

= 0.0134 + 0.0668 + 0.1559

= 0.2361