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.

(Please help!!)

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%

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.