Question

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3988 grams and a variance of 119,716 . if a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4226 grams.

Answer 1

The probability that a randomly selected newborn baby boy will weigh less than 4226 grams is approximately 75.49%, calculated using the z-score and the standard normal distribution.

Step-by-step explanation:

The question involves finding the probability that a newborn baby boy's weight is less than 4226 grams when the weights are normally distributed with a mean of 3988 grams and a variance of 119,716 grams^2. To find this probability, we calculate the z-score and use the standard normal distribution.

First, we find the standard deviation by taking the square root of the variance. The standard deviation (σ) is √119,716 ≈ 346 grams.

Next, we calculate the z-score using the formula:

Z = (X - μ) / σ

Z = (4226 - 3988) / 346

Z ≈ 0.688

Now, we look up this z-score in the standard normal distribution table or use a calculator with a normal distribution function to find the probability, which is the area under the curve to the left of this z-score.

The probability for a z-score of 0.688 is approximately 0.7549, which means there's a 75.49% chance that a randomly selected newborn baby boy will weigh less than 4226 grams.