Question

70% of all us households have vcrs. In a random sample of 15 households, what is the probability that the number of households with vcrs is between 10 and 12, inclusive?

Answer 1

Therefore the probability of 10 - 12 inclusive = 0.20613 + 0.21862 + 0.17004

= 0.59479

+ 59.5% to one place of decimals

Explanation:

P(exactly 10) = 15C10 * (0.70)^10 * (0.30)^5

=15! / (10! * 5!) * (0.70)^10 * (0.30)^5

= (15*14*13*12*11) /(5*4*3*2*1) * (0.70)^10 * (0.30)^5

= 0.20613

P(exactly 11) = 15C11 * (0.70)^11 * (0.30)^4

= (15*14*13*12)/(4*3*2*1) *(0.70)^11 *(0.30)^4

= 0.21862

P(exactly 12) = 15C12 * (0.70)^12 * (0.30)^3

= (15*14*13)/(3*2*1) * (0.70)^12 * (0.30)^3

= 0.17004