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According to a recent survey, 93 out of 120 of Americans over the age of 25...

According to a recent survey, 93 out of 120 of Americans over the age of 25 have earned a high school diploma.
what is the sampling distribution of the sample proportions? (show work step by step/- Find the mean and the standard deviation for the sample proportion.) just trying to check my answers to see if theyre correct thank you
Math   Statistics-And-Probability   
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Answer: We have given that, according to recent survey, 93 out of 120 of Americans over the age of 25 have earned a high school diploma. We know that, if repeated random samples of a given size n are taken from a population of values for a categorical variable, where the proportion in the category of interest is p, then the mean of all sample proportions (p-hat) is the populatlon proportion (p).

Therefore mean of sample proportion is p=93/120. ==> p=0.775.

Standard deviation for proportion:

Therefore standard deviatation for above example is squr((0.775(1-(0.775))/120) = 0.040.

Note:

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