Question

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3276 grams and a variance of 53,361. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 3738 grams. Round your answer to four decimal places.

a) 0.8413
b) 0.1587
c) 0.5000
d) 0.8417

Answer 1

To find the probability that the weight of a newborn baby boy born at a local hospital will be less than 3738 grams, we can calculate the z-score and use the standard normal distribution table. The probability is approximately 0.4207.

Step-by-step explanation:

To find the probability that the weight of a randomly selected newborn baby boy will be less than 3738 grams, we need to calculate the z-score and then use the standard normal distribution table.

The z-score is calculated using the formula z = (x - μ) / σ, where x is the weight, μ is the mean weight, and σ is the standard deviation. In this case, x = 3738 grams, μ = 3276 grams, and σ = √(53361 grams^2) ≈ 231.06 grams.

Plugging in these values, we get z = (3738 - 3276) / 231.06 ≈ 0.1992.

Now, we can use the standard normal distribution table to find the probability associated with the z-score. Looking up the z-score of 0.1992 in the table, we find that the probability is approximately 0.5793.

However, we want the probability that the weight is less than 3738 grams, so we need to subtract this probability from 1. Therefore, the probability is approximately 1 - 0.5793 = 0.4207.