The ages of the 32 recruits in police academy are normally distributed with a mean of 27 with a standard deviation of 2. what is the probability that a recruit is at least 31 years old?

Since it's a sample size, we use x, as the mean and s= standard deviation
            _
Given:  x =27, s = 2 and total sample = 32.
Probability that a recruit is at least 31 years old?

Let's calculate the Z score :
              _
         X - x              31 - 27
Z =  → Z =  → Z = 2 (now look up in the Z score table,
           s                      2

Area (Z=2) =0.9772 , but Z ≥ 2  (at least) , then :
Area (Z≥2) = Area (Z≤ - 2)  = 0.0228

P(≥31)= 0.0228

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