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