according to a website, the main weight of an adult member of particular breed of dog is 146 pounds assume the distribution of voices normal with the standard deviation of 10 The standard score associated with the weight of 166 pounds is z equals

To find the standard score (z-score) associated with a weight of 166 pounds, we use the formula:

\[
z = \frac{x - \mu}{\sigma}
\]

Where:
- \( x \) is the value of the weight (166 pounds),
- \( \mu \) is the mean (146 pounds),
- \( \sigma \) is the standard deviation (10 pounds).

Let's plug in the values:

\[
z = \frac{166 - 146}{10} = \frac{20}{10} = 2
\]

Thus, the standard score (z) associated with a weight of 166 pounds is \( z = 2 \).

Would you like further details or clarification?

Here are 5 related questions:
1. What does a z-score of 2 signify in terms of distribution?
2. How do you calculate probabilities using the z-score?
3. Can you determine the percentage of data above or below a certain z-score?
4. How do you interpret negative z-scores in a normal distribution?
5. How does changing the standard deviation affect the z-score?

**Tip:** The z-score tells you how many standard deviations a data point is from the mean; a z-score of 2 means the data point is two standard deviations above the mean.

According to a website, the main weight of an adult member of a particular breed of dog is 146 pounds. Assume the distribution of weights is normal with a standard deviation of 10. The standard score associated with the weight of 166 pounds is z equals?

Learn how to calculate the z-score for a dog's weight of 166 pounds, assuming a normal distribution with a mean of 146 pounds and a standard deviation of 10. This problem demonstrates key statistical concepts like z-scores and normal distribution, suitable for students in Grades 10-12.

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