Question

The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 16 years, the

standard deviation is 1.7 years.

Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a gorilla living longer than 14.3

years.

Percent ____

Answer 1

68%

Explanation:

Empirical rule formula

= 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

From the above question,

Mean = 16 years

Standard deviation = 1.7 years

Score = 14.3 years

We have to find the number of standard deviation to determine the percentage

Hence,

14.3 = 16 - 1.7x

Collect like terms

1.7x = 16 - 14.3

1.7x = 1.7

x = 1.7/1.7

x = 1

This means the data falls within 1 standard deviation from the mean hence, the probability of the gorilla living longer than 14.3 years is 68%