Suppose that in a certain metropolitan area, 90% of all households have cable TV. Let x denote the number among four randomly selected households that have cable TV. Then x is a binomial random variable with n = 4 and p = 0.9. (Round your answers to four decimal places.)

a. Calculate p(2) = P(x = 2).
b. Interpret this probability.

i. This is the probability that at least 2 out of 4 selected households have cable TV.
ii. This is the probability that exactly 2 out of 10 selected households have cable TV.
iii. This is the probability that exactly 2 out of 4 selected households have cable TV.
iv. This is the probability that at least 2 out of 10 selected households have cable TV.

c. Calculate p(4), the probability that all four selected households have cable TV.
d. Determine P(x ≤ 3).

Ithink number to is 1 inch=5 miles

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12