Using the normal distribution, we know that the likelihood of a lizard living longer than 2.5 years is 16%.
The normal distribution is the correct name for a probability bell curve alone.
A normal distribution has a mean of zero and a standard deviation of one. Its kurtosis is 3, and its skew is 0.
Not all normal distributions are symmetrical, despite the fact that all symmetrical distributions are normal.
So, a lizard's average lifespan is 3.1 years, with a 0.6-year standard deviation.
Lizard u = 3.1 on average.
0.6 is the standard deviation.
To determine the probability that a lizard would live 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
Use the empirical rule to calculate the probability.
100% of the total area (since total probability always is 1)
The area from p(X > p) = 50% from to area between () and (+) equals 68%.
Area between (μ−σ) and μ is p((μ−σ) < X < μ) =34%
Hence,
p(X< (μ−σ)) = 1 − (p((μ−σ) < X < μ) + p(X > μ))
p(X< (μ−σ)) = 1 − (0.34 + 0.5)
p(X< (μ−σ)) = 0.16
Therefore, using the normal distribution, we know that the likelihood of a lizard living longer than 2.5 years is 16%.
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