Question

A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 673 babies born in New York. The mean weight was 3458 grams with a standard deviation of 903 grams. Assume that birth weight data are approximately bell-shaped.

a) Determine the z-score for a baby with a birth weight of 4000 grams.
b) Calculate the probability that a randomly selected baby weighs less than 3000 grams.

Answer 1

The z-score for a baby with a birth weight of 4000 grams is approximately 0.598. The probability that a randomly selected baby weighs less than 3000 grams is approximately 0.4801 or 48.01%.

Step-by-step explanation:

To determine the z-score for a baby with a birth weight of 4000 grams, we can use the formula: z = (x - μ) / σ, where x is the birth weight, μ is the mean weight, and σ is the standard deviation. Plugging in the values, we get: z = (4000 - 3458) / 903 ≈ 0.598. Therefore, the z-score for a baby with a birth weight of 4000 grams is approximately 0.598.

To calculate the probability that a randomly selected baby weighs less than 3000 grams, we need to find the area to the left of 3000 on the bell-shaped distribution curve. We can use the z-score formula again: z = (x - μ) / σ. Plugging in the values, we get: z = (3000 - 3458) / 903 ≈ -0.051. Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than -0.051 is approximately 0.4801. Therefore, the probability that a randomly selected baby weighs less than 3000 grams is approximately 0.4801 or 48.01%.