This is a confidence interval problem where we are looking for the number from the given options which falls inside the upper 95% confidence interval.
A confidence interval is <span>a range of values so defined that there is a specified probability that the value of a parameter lies within it.
Here, we are to find </span>a range of values so defined that there is a 95% probability that the value of <span>Cynthia's standardized test score</span> lies within it.
The 95% confidence interval of the mean is given by
where:
is the sample mean, 1.96 is the standard normal score associated with 95%,
is the standard deviation and n is the sample size.
Since, the sample size is unknown, we reduce the formular to
Therefore, the 95% confidence interval is
Now, since we are interested with the upper confidence, we have that the value of Cynthia's test score is between 180 and 180 + 29.4, i.e. between 180 and 209.4
Therefore, from the options given <span>the score that Cynthia would most likely get on a standardized test is 205.
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