Fifteen percent of new residential central air conditioning units installed by a supplier
need additional adjustments requiring a service call. Assume that a recent sample of seven such units
constitutes a Bernoulli process. Interest centers on X, the number of units among these seven that need
additional adjustments.
(92) The probability that exactly 2 units need additional adjustments is about:
(A) 0.15 (B) 1.05 (C) 0.21 (D) 0.16
(93) The probability that at least 2 units need additional adjustments is about:
(A) 0.15 (B) 0.926 (C) 1.05 (D) 0.16
(94) The mean number of units that need additional adjustments is:
(A) 0.15 (B) 0.32 (C) 1.05 (D) 0.16
(95) The variance of X is:
(A) 0.8925 (B) 0.6654 (C) 0.0214 (D) 0.3225

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).