Final answer:
The probability of an Asian Elephant living longer than 80 years can be calculated using the z-score and the standard normal distribution table or calculator. To determine if a life span of at most 21 years is unusual, the z-score for 21 years can be compared against the standard normal distribution. These calculations rely on the given mean life span and standard deviation.
Step-by-step explanation:
Calculating the Probability for the Life Span of Aslan Elephants
The questions pertain to the normal distribution and probabilities involving the life span of Asian Elephants (Elephas Maximus). Given the mean life span (56.3 years) and the standard deviation (14.8 years), we can calculate the probability of events related to the elephant's life span.
Probability of Living Longer Than 80 Years
To find the probability of an Asian Elephant living longer than 80 years, we apply the z-score formula: z = (X - µ) / σ, where X is the value of interest (80 years), µ is the mean life span, and σ is the standard deviation. First, we calculate the z-score: z = (80 - 56.3) / 14.8. Then, using the z-score, we check the standard normal distribution table or use a calculator to find the corresponding probability.
Unusual Life Span
Regarding whether it would be unusual for an Asian Elephant to live at most 21 years, we again calculate the z-score for 21 years and compare it to the standard normal distribution. If the resulting z-score corresponds to a very low percentile, it suggests that living at most 21 years is indeed unusual for this species.