The proportion of adult women in a certain geographical region is approximately
ID: 3219562 • Letter: T
Question
The proportion of adult women in a certain geographical region is approximately 51%. A marketing survey telephones 200 people at random. Complete parts a through a below. a) What is the sampling distribution of the observed proportion that are women? A. Approximately Normal B. Approximately Exponential C. Approximately Uniform D. None of these b) What is the standard deviation of that proportion? c) Would you be surprised to find 62% women in a sample size of 200? A. That is surprising because 0.52 is more than two standard deviations above mean. B. That is not surprising because 0.52 is less than one standard deviation above the mean. C. That is surprising because 0.52 is a less than one standard deviation above mean. D. That is not surprising because 0.52 is none than one standard deviation above mean. d) Would you be surprised to find 30% women in a sample of 200? A. That is not surprising because 0.39 is less than two standard deviation below the mean. B. That is surprising because 0.39 is more than three standard deviations below the mean. C. That is not surprising because 0.39 is more than three standard deviations below the mean. D. That is surprising because 0.39 is less than two deviations below the mean e) Would you be surprised to find that there were fewer than 74 women in the sample? Select the correct choice below and fill in the answer box within your choice. A. That is surprising since 74 women represents a proportion of, which is less than two standard deviations below the mean.Explanation / Answer
Solution:-
a) option A. Approximately normal
b) Variance of Binomial Distribution is given by
n*p*(1-p) = 200*0.51*(1-0.51) = 200*0.51*0.49 = 49.98
Then standard deviation is square root of variance
= sqrt(49.98)
= 7.07
c) option B
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