Question

Suppose that the weight of male babies less than 2 months old is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. What proportion of babies weigh less than 10.82 pounds? Write only a number as your answer. Round to 4 decimal places (for example 0.0048). Do not write as a percentage.

Answer 1

The proportion of male babies less than 2 months old weighing less than 10.82 pounds, given a normal distribution with a mean of 11.5 pounds and a standard deviation of 2.7 pounds, is approximately 0.4005.

Step-by-step explanation:

To find the proportion of male babies less than 2 months old weighing less than 10.82 pounds, we can utilize the normal distribution of their weights. Given that the mean weight (μ) is 11.5 pounds and the standard deviation (σ) is 2.7 pounds, we can calculate the z-score for a weight of 10.82 pounds.

The formula for the z-score is:
z = (X - μ) / σ
where X is the weight of interest, μ is the mean, and σ is the standard deviation.

For a weight of 10.82 pounds, the z-score calculation would be:
z = (10.82 - 11.5) / 2.7 = -0.68 / 2.7 = -0.2519

Using z-score tables or a calculator, we can find the proportion of the normal distribution that lies below this z-score. The proportion of male babies weighing less than 10.82 pounds is approximately 0.4005.