Question

A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 99 students in the high school and found a mean savings of 3800 dollars with a standard deviation of 500 dollars. Use the normal distribution/empirical rule to estimate a 95

Answer 1

To estimate a 95% confidence interval for the mean amount of money that each student had saved, we can use the normal distribution. The empirical rule states that approximately 95% of the data falls within 2 standard deviations of the mean. Given the mean savings of $3800 with a standard deviation of $500, the confidence interval is between $3701.54 and $3898.46.

Step-by-step explanation:

To estimate a 95% confidence interval for the mean amount of money that each student had saved, we can use the normal distribution. The empirical rule states that approximately 95% of the data falls within 2 standard deviations of the mean.

Given that the mean savings is $3800 with a standard deviation of $500, we can calculate the confidence interval as follows:

1. Calculate the standard error: SE = standard deviation / square root of sample size = $500 / sqrt(99) = $50.25
2. Calculate the margin of error: MOE = 1.96 * SE = 1.96 * $50.25 ≈ $98.46
3. Calculate the lower and upper bounds of the confidence interval: Lower bound = mean - MOE = $3800 - $98.46 ≈ $3701.54; Upper bound = mean + MOE = $3800 + $98.46 ≈ $3898.46

Therefore, we can estimate with 95% confidence that the mean amount of money each student has saved is between $3701.54 and $3898.46.