Question

The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20. 820. 820, point, 8 years; the standard deviation is 3. 13. 13, point, 1 years.

Answer 1

A z-score of 23.9 years must be located in the gorillas' lifespans in a specific zoo's typical normal distribution.

Define the term normal distribution?

• A data collection with a normal distribution is put up so that the majority of the values cluster as in midpoint of the range and the remaining values taper off symmetrically in either direction.

The equation can be used to determine the z score.

z = (x - μ)/σ

In which,

• X is age 23.9.
• The typical gorilla life span is M. (20.8 years).
• The standard deviation is s. (3.1 years).

Then,

z = (23.9 - 20.8)/3.1

z = 1

According to the empirical rule, 68% of lifespans are within one standard deviation of the mean.

Half of it, 68/2 = 34% %, is on the right side of the mean's standard deviation.

Given that the likelihood of a gorilla lasting less than 23.9 years is 50%.

A gorilla's lifespan being less than the norm means is;

50% + 34% = 84% sits below z-score 1.

Thus, the probability of a gorilla living less than 23.9 years is 84%.

To know more about the normal distribution, here

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The correct question is-

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.