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CetaNow is a conservationist organization that monitors the health of whale and dolphin populations worldwide. As part of their work, they are modeling the lengths of blue whale calves that will be born over the next decade. For their model, CetaNow is using a normal distribution with a mean of 281 in and a standard deviation of 40in.

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Answer to a math question CetaNow is a conservationist organization that monitors the health of whale and dolphin populations worldwide. As part of their work, they are modeling the lengths of blue whale calves that will be born over the next decade. For their model, CetaNow is using a normal distribution with a mean of 281 in and a standard deviation of 40in.

Expert avatar
Seamus
4.9
98 Answers
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%.

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