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Answer:
d) No, this would not be unusual because 46% is only 1.2 standard errors from 40%.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If the z-score is higher than 2 or lower than -2, X is unusual.
In this question:
Mean = 40%. So
Standard error = 5%. So
Is 46% unusual?
We have to find Z when X = 0.46. So
1.2 is lower than 2, that is, it is only 1.2 standard deviations from the mean. So 46% is not unusual.
So the correct answer is:
d) No, this would not be unusual because 46% is only 1.2 standard errors from 40%.