Answer :
The probability that the average weight of 23 randomly selected babies falls between 3000 grams and 3700 grams can be calculated using the Central Limit Theorem and the assumption of a normal distribution.
The Central Limit Theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, if the sample size is large enough. With this in mind, we can approximate the distribution of the average weight of 23 randomly selected babies as a normal distribution.
To find the probability that the average weight falls between 3000 grams and 3700 grams, we need to standardize the values using the mean and standard deviation of the population. Let's assume that the mean weight of babies is μ and the standard deviation is σ.
Using the Central Limit Theorem, we know that the mean of the sample means will be equal to the population mean (μ) and the standard deviation of the sample means will be equal to the population standard deviation divided by the square root of the sample size (σ/√n).
Next, we can standardize the values of 3000 grams and 3700 grams by subtracting the population mean and dividing by the standard deviation of the sample means. Let's denote the standardized values as Z1 and Z2.
Once we have Z1 and Z2, we can look up the corresponding probabilities from the standard normal distribution table or use statistical software to calculate the area under the curve between Z1 and Z2.
The calculated probability will give us the likelihood that the average weight of 23 randomly selected babies falls between 3000 grams and 3700 grams.
Learn more about Central Limit Theorem here:
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