The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the

standard deviation is 3.1 years.

Use the empirical rule (68 – 95 - 99.7%) to estimate the probability of a gorilla living less than 23.9

years.

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dogacandu dogacandu · Answer 1 · 2019-12-25T19:48:18+01:00

Answer:

The probability of a gorilla living less than 23.9 years is 0.84 (84%)

Step-by-step explanation:

We need to find the z-score of 23.9 years in the standard normal distribution of the lifespans of gorillas in a particular zoo.

z score can be calculated using the equation

[tex]z=\frac{X-M}{s}[/tex] where

Then [tex]z=\frac{23.9-20.8}{3.1}=1[/tex]

Empirical rule states that 68% of the lifespans lie within 1 standard deviation from the mean.

Half of it, [tex]\frac{68}{2}=34[/tex]% lies right side of 1 standard span of the mean.

Since lifespan less than mean is 50%, 50%+34% =84% lies less than z-score 1, that is the probability of a gorilla living less than 23.9 years.

okpalawalter8 okpalawalter8 · Answer 2 · 2022-04-19T11:43:14+02:00

The probability of a gorilla living less than 23.9 years is mathematically given as

P(Z < 1) = 84%

Question Parameter(s):

The average gorilla lives 20.8 years;

the standard deviation is 3.1 years.

Generally, the equation for the Zscore is mathematically given as

[tex]The Zscore = (x - \=x) / \sigma[/tex]

Therefore

P(x < 23.9) = (23.9 - 20.8) / 3.1

P(x < 23.9) = 1

In conclusion

P(Z < 1) = 0.84134

P(Z < 1) 0.84134 * 100%

P(Z < 1) = 84%