Final answer:
To find the probability of a sample mean being 2859 grams or lower, we calculate the z-score for the sample mean and refer to the standard normal distribution. If the resulting probability is very small or the z-score is beyond the common cutoffs, the sample mean is unusual.
Step-by-step explanation:
The question concerns the probability of sampling a mean birth weight from a normal distribution and whether a sample mean of 2859 grams is unusual. Given a population with a mean weight of 3058 grams and standard deviation of 708 grams, we can calculate the probability of a random sample of 100 newborn girls having a mean birth weight of 2859 grams or lower using the standard normal distribution (Z-distribution).
To determine the z-score for the observed sample mean:
Z = (X - μ) / (σ / sqrt(n))
Where:
- X = sample mean = 2859 grams
- μ = population mean = 3058 grams
- σ = population standard deviation = 708 grams
- n = sample size = 100
The Z-score calculated will then be used to find the probability from the Z-table.
If the probability of obtaining a sample mean of 2859 grams or lower is very small, it would suggest that such a result is indeed unusual. If the calculated Z-score is beyond the typical cutoffs (such as -1.96 or +1.96 for a 95% confidence interval in a two-tailed test), then a sample mean of 2859 grams would be considered unusual.