SOLUTION: Scores on a standardized exam are known to follow a normal distribution with a standard deviationσ of = 8. A researcher randomly selects 84 students and finds their mean exam sco
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Question 1168124: Scores on a standardized exam are known to follow a normal distribution with a standard deviationσ of = 8. A researcher randomly selects 84 students and finds their mean exam score to be (X with the bar over it) = 78. How confident are you that the mean score for all students taking the exam is in the interval (76.702, 79.298)?
confidence level= Answer by Theo(13342) (Show Source):
the standard error is equal to the population standard deviation divided by the sample size.
this is equal to 8 / sqrt(84) = .8728715609
use a normal distribution calculator to find the proportion of scores between 76.702 and 79.298 when the mean score is 78 and the standard error of a sample size of 84 is equal to .8728715609.
your result will be that the proportion is equal to .8629972264.
that's your confidence level.
you are confident that 86.3% of samples of size 84 will have a mean that falls between 76.702 and 79.298.
100 - 86.3 = 13.7% of the samples will have a mean that falls outside these limits.
half of the 13.7% will fall below 76.782 and the other half of the 13.7% will fall above 79.298.
here's a display of the calculator results, rounded to whatever rounding rules the calculator has.
the online calculator says that the probability that the scores will be within those limits is .863.
round .8629972264. to 3 decimal digits and it becomes .863.
