Question

Asked if he has any regrets about the way he's handled the coronavirus crisis so far, President Trump said no — and he cited polling to back him up. Trump has hit his highest approval rating since becoming president – 47% according to an average of the polls. For a random sample of size n = 50 citizens, is it safe to assume that the distribution of sample proportions is bell shaped?

Answer 1

Yes, for a random sample of size n = 50 citizens, is it safe to assume that the distribution of sample proportions is bell-shaped. This is because the sample size 50 is a large enough sample. Also

• n*p = 50*0.47=25.5 >= 5
• n*p*(1-p) = 50*0.47*(1-0.47) =12.455 >=5

Also consider the following graph for n=50 and p=0.47 which is clearly bell shaped.

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