Answer :
Final answer:
The z-score that corresponds to a 97% confidence interval is d) 2.58. This value is used to capture the central 97% of the data in a normal distribution, indicating the extent to which we must go out from the mean on either side.
Explanation:
The question asks: What z-score goes with a 97% confidence interval? To answer this, it's crucial to understand how z-scores relate to confidence intervals in statistics. Confidence intervals are used to estimate the range in which a population parameter is expected to fall with a certain degree of confidence. The 97% confidence interval specifically means we are looking for the z-score that captures 97% of the data under the normal distribution curve, leaving 1.5% of the data on each tail.
The correct answer is d) 2.58. When constructing a 97% confidence interval, the z-score that corresponds to capturing the central 97% of the normal distribution is approximately 2.58. This means that to capture 97% of the data around the mean, one would go out 2.58 standard deviations on either side of the mean.
This z-score directly correlates with the way confidence intervals are constructed and used in statistics to provide a range estimate that a parameter lies within with a certain degree of confidence.
