37 packages are randomly selected from packages received by a parcel service. the sample has a mean weight of 10.3 pounds and a standard deviation of 2.4 pounds. what is the 95% confidence interval for the true mean weight, µ, of all packages received by the parcel service?

True mean = mean+/- Z*(SD/sqrt (n))

Where
Z = 1.96 at 95% confidence interval
Mean = 10.3 pounds
SD = standard deviation = 2.4 pounds
n= sample size = 37 packages

Substituting;
True mean range = 10.3+/- 1.96 * 2.4/Sqrt (37) =10.3+/- 0.77 = 9.53<mean<11.07

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