An article in an educational journal discussing a non-conventional high school reading program reports, with 95% confidence, the average score on the reading portion of the SAT is between 520 and 560. The study was based on a random sample of 20 students and it was assumed that SAT scores would be approximately normally distributed. Determine the average SAT reading score of the 20 students sampled.

The confidence interval for the mean is given by the following formula:

  (1)

For this case the confidence interval at 95% of confidence calculated was (520,560)

And from this case we can estimate the average with the following formula:

Since the average represent the midpoint of the interval, if we replace we got:

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n=20 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

For this case the confidence interval at 95% of confidence calculated was (520,560)

And from this case we can estimate the average with the following formula:

Since the average represent the midpoint of the interval, if we replace we got: