Question

The lifespans of seals in a particular zoo are normally distributed. The average seal lives 13.8 years; the standard deviation is 3.23 years. Use the empirical rule (68-95-99.7%) to estimate the probability of a seal living less than 7.4 years.

a) Approximately 2.5%
b) Approximately 16%
c) Approximately 84%
d) Approximately 97.5%

Answer 1

To estimate the probability of a seal living less than 7.4 years, calculate the z-score using the formula (x - μ) / σ with x = 7.4, μ = 13.8, and σ = 3.23. Look up the z-score in the z-table to find the probability, which is approximately 2.5%.

Step-by-step explanation:

To estimate the probability of a seal living less than 7.4 years using the empirical rule, we need to calculate the z-score and look it up in the z-table.

The formula for calculating the z-score is: z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, x = 7.4, μ = 13.8, and σ = 3.23.

Calculating the z-score: z = (7.4 - 13.8) / 3.23 = -1.9869 (approx.)

Looking up the z-score of -1.9869 in the z-table, we find that the probability is approximately 0.0247.

Therefore, the approximate probability of a seal living less than 7.4 years is 0.0247, which is approximately 2.5%.