Suppose the heights of 18-year-old men are approximately normally distributed, with mean 67 inches and standard deviation 5 inches. (a) what is the probability that an 18-year-old man selected at random is between 66 and 68 inches tall? (round your answer to four decimal places.) (b) if a random sample of twelve 18-year-old men is selected, what is the probability that the mean height x is between 66 and 68 inches? (round your answer to four decimal places.)

(a) The probability that an individual is within 1 standard deviation of the mean is 0.1585

(b) The probablity that the mean of a sample of 12 is within 1 standard deviation of the population mean is 0.5116

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