Question

The average birth weight of domestic cats is about 3 ounces. Assume that the distribution of birth weights is Normal with a standard deviation of 0.3 ounce. Find the birth weight of cats at the 90th percentile.

Answer 1

To find the birth weight of cats at the 90th percentile, use the concept of the standard normal distribution. Calculate the z-score corresponding to the 90th percentile, and then substitute it into the formula to find the birth weight.

Step-by-step explanation:

To find the birth weight of cats at the 90th percentile, we can use the concept of the standard normal distribution. Since the distribution of birth weights is normal with a mean of 3 ounces and a standard deviation of 0.3 ounces, we can use a z-table or a calculator to determine the z-score corresponding to the 90th percentile. The z-score can then be used to find the corresponding birth weight.

1. Calculate the z-score using the formula: z = (x - μ) / σ, where x is the birth weight, μ is the mean, and σ is the standard deviation.
2. Use a z-table or a calculator to find the z-score corresponding to the 90th percentile. The z-score will give you the number of standard deviations away from the mean.
3. Substitute the z-score into the formula and solve for x: x = z * σ + μ.

Using the z-table or a calculator, you can find that the z-score corresponding to the 90th percentile is approximately 1.28. Substituting this value into the formula, we get x = 1.28 * 0.3 + 3 = 3.384 ounces. Therefore, the birth weight of cats at the 90th percentile is approximately 3.384 ounces.