What percentage of blue whales have a mass of over $$ 186,000 \mathrm{~kg} ? $$

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We assume that the masses of blue whales are normally distributed. Suppose the mass $$X$$ (in kg) of a blue whale follows

$$
X \sim N(\mu, \sigma)
$$

with mean $$\mu = 150\,000$$ kg and standard deviation $$\sigma = 24\,000$$ kg. We wish to find the percentage of blue whales that have a mass greater than $$186\,000$$ kg.

**Step 1. Compute the $$z$$-score**

The $$z$$-score corresponding to $$X = 186\,000$$ kg is given by

$$
z = \frac{X - \mu}{\sigma} = \frac{186\,000 - 150\,000}{24\,000} = \frac{36\,000}{24\,000} = 1.5.
$$

**Step 2. Find the probability that $$z > 1.5$$**

Using a standard normal distribution table or calculator, we find

$$
P(Z > 1.5) \approx 0.0668.
$$

This means that approximately $$6.68\%$$ of blue whales have a mass greater than $$186\,000$$ kg.

**Final Answer**

Approximately $$6.7\%$$ of blue whales have a mass greater than $$186\,000$$ kg.
Approximately 6.7% of blue whales weigh more than 186,000 kg.

What percentage of blue whales have a mass of over \( 186,000 \mathrm{~kg} ? \)

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