There is a 95% chance that the true mean is between 1 and 3, if our sample's 95% confidence interval is between 1 and 3.

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There is a 95% chance that the true mean is between 1 and 3, if our sample&#039;s 95% confidence interval is between 1 and 3.&amp;nbsp;

Andre BalkonE · Accepted Answer

To solve the given problem, let&#039;s first understand the concept of a confidence interval.A confidence interval is a range of values within which we can be reasonably confident that the true population parameter lies. In this case, we are interested in estimating the true mean.Given that the sample&#039;s 95% confidence interval is between 1 and 3, we can interpret this as follows:Let μ represent the true population mean.The given confidence interval, [1,3], means that we are 95% confident that the true population mean μ falls within this interval.Mathematically, this can be expressed as:P(1≤μ≤3)=0.95To solve for the probability, we need to find the Z-score associated with a 95% confidence level. The Z-score corresponds to the number of standard deviations away from the mean.The Z-score for a 95% confidence level can be found using a standard normal distribution table or calculator. For a two-tailed test, the Z-score is approximately 1.96.Now, we can express the confidence interval in terms of Z-scores:1≤μ≤3Dividing both sides by the standard deviation, σ, gives:1σ≤μσ≤3σSince we are dealing with a standard normal distribution, the Z-scores are equivalent to the standard deviations:−1.96≤μσ≤1.96Now, we can solve for the standard deviation, σ:μσ=1.96Solving for σ:σ=μ1.96Therefore, the standard deviation is equal to the true mean divided by 1.96.

There is a 95% chance that the true

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