To find the probability of blue whale calves being born with a length greater than 300 inches, we need to calculate the z-score using the z-score formula:
z = \frac{x - \mu}{\sigma}
where:
x = 300 inches (desired length)
\mu = 281 inches (mean length)
\sigma = 40 inches (standard deviation)
Plugging in the values:
z = \frac{300 - 281}{40} = \frac{19}{40} = 0.475
Next, we look up the z-score in the standard normal distribution table to find the probability.
The probability of a z-score of 0.475 in a standard normal distribution table is approximately 0.681 (or 68.1%).
Therefore, the probability of a blue whale calf being born with a length greater than 300 inches is approximately 0.681 or 68.1%.
\textbf{Answer:} The probability is approximately 0.681 or 68.1%.