The ABC Manufacturing Corporation produces steel rods. Due to manufacturing defects, there is

some small variation in the lengths of the rods.

The lengths of the rods have a Normal distribution

with mean

cm. and standard deviation

cm. Suppose one steel rod is randomly

selected from a batch and measured.

For each problem #1 – 3, show any relevant z-score calculation, draw a normal curve, label the mean

of the distribution, and shade in the region that illustrates the area representing the given probability.

1. Find the probability that a randomly-selected steel rod has a length less than 24.90 cm. (3 pts)

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