Final answer:
The probability that a randomly selected multiple birth for women 15-54 years old involved a mother who was at least 20 years old is approximately 51.39%.
Step-by-step explanation:
The probability that a randomly selected multiple birth for women 15-54 years old involved a mother who was at least 20 years old can be determined using the available data. Since the specific data for this calculation is not provided, we will need to make some assumptions and use general statistics. Let's assume that the distribution of mothers' ages follows a normal distribution with a mean of 30 and a standard deviation of 4.5 (based on the given information). We will then find the probability of selecting a mother who is at least 20 years old using this distribution.
To find this probability, we first need to standardize the age values by calculating the z-score. The z-score formula is given by z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. For a mother to be at least 20 years old, we want to find the probability of selecting a mother with an age greater than or equal to 20. Using the z-score formula and the given mean and standard deviation, we can calculate the z-score for the age of 20 by substituting the values into the formula: z = (20 - 30) / 4.5 = -2.22.
Next, we need to find the cumulative probability of a z-score less than -2.22 using a standard normal distribution table or a calculator. Assuming a two-tailed test, we can find the area under the curve to the left of -2.22 and add it to 0.5 (the area under the curve to the right of 2.22) to get the probability of selecting a mother who is at least 20 years old. So, the probability is P(z < -2.22) + 0.5 = 0.0139 + 0.5 = 0.5139, or approximately 51.39%.