The lifespans of lizards in a particular zoo are normally distributed. The average lizard lives 3.1 years; the standard deviation is 0.6 years. Use the empirical rule (68-95-99.7%) to estimate the probability of a lizard living longer than 2.5 years.

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Thus probability of a lizard living longer than 2.5 yearsb= 16%

Step-by-step explanation:

The average lizard lives 3.1 years; the standard deviation is 0.6 years.

u=3.1, σ=0.6

to estimate the probability of a lizard living longer than 2.5 years = p(X<2.5)

μ+aσ=2.5

3.1+a(0.6)=2.5

a(0.6)=−0.6

a=−1

Usimg emphirical rule to calculte the probability,

The total area = 100% (as total probability is always 1)

Area from  μ to ∞  =  p(X>μ)  = 50%

Area between  (μ−σ)  and  (μ+σ)  = 68%  

Area between  (μ−σ)  and  μ  is  p((μ−σ)<X<μ)  =   =34%  

Therefore,

p(X<(μ−σ))=1−(p((μ−σ)<X<μ)+p(X>μ)) = 1−(0.34+0.5) = 0.16  

Thus probability of a lizard living longer than 2.5 yearsb= 16%

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