To find the probability that a randomly selected white-tailed deer will weigh less than 149 pounds, we can use the Z-score formula. The Z-score tells us how many standard deviations a specific value is from the mean.
The Z-score is calculated as follows:
\[ Z = \frac{(X - \mu)}{\sigma} \]
where:
- \(X\) is the value we are interested in (149 pounds),
- \(\mu\) is the mean weight (140.3 pounds),
- \(\sigma\) is the standard deviation (7.2 pounds).
Plugging in the values:
\[ Z = \frac{(149 - 140.3)}{7.2} = \frac{8.7}{7.2} \approx 1.2083 \]
Next, we look up the Z-score of approximately 1.21 in the standard normal distribution table (or use a calculator or software that provides the cumulative distribution function for the normal distribution).
Looking up the Z-score of 1.21 typically gives us approximately 0.8869 or 88.69%.
So, the probability that a randomly selected deer will weigh less than 149 pounds is about 88.7%.
The correct response is 88.7%.