Question

The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. use z-scores to determine which birth weight could be considered unusual.

Answer 1

An unusual birth weight for twins, based on the provided mean of 2353 grams and standard deviation of 647 grams, would be considered if the weight is lower than 1059 grams or higher than 3647 grams. These thresholds are calculated using z-scores that are more than 2 standard deviations away from the mean.

Step-by-step explanation:

The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. To determine which birth weight could be considered unusual, we use z-scores. A z-score indicates how many standard deviations an element is from the mean.

A common threshold to define an 'unusual' z-score is one that is more than 2 standard deviations away from the mean (either below or above). This corresponds to z-scores less than -2 or greater than +2.

To calculate this for the twins' birth weights, you use the formula:

Z = (X - μ) / σ

Where Z is the z-score, X is the weight of the twins, μ is the mean, and σ is the standard deviation.

Therefore, a birth weight is considered unusual if:

Z < -2 (which translates to a weight of 2353 - 2(647) = 1059 grams)

or

Z > +2 (which translates to weight of 2353 + 2(647) = 3647 grams).

Thus, any twin with a birth weight lower than 1059 grams or higher than 3647 grams would be considered to have an unusual birth weight.

Answer 2

Z-scores allow us to determine how far from the mean value is the data point given. It is usually considered an "unusual value" if the data has a z-score of that has an absolute value greater than 2. Z-scores are calculated through the following equation,
z-score = (data point - mean) / standard deviation