ap statistics - According to the town gardening association 86 percent of the over 15, 000 families with vegetable gardens in the town grow tomatoes suppose we took random samples of 100 families each from this population and calculated the proportion \widehat{p} of sampled families who grow tomatoes for each sample

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

We need at least 10 expected "successes" and at least 10 expected "failures" for the sampling distribution of the sample proportion to be approximately normal:

np≥10 and n(1−p)≥10

Our sample size is n=100 families, and p=0.86 since 86% of the population grows tomatoes.

Expected successes: np =100 (0.86) = 86 ≥ 10.

Expected failures: n(1−p) = 100 (1−0.86)= 14 ≥ 10.

So, we have a normal sampling distribution because we expect at least 10 successes and 10 failures per sample.

So, option C is the correct choice.

Which of the following distributions is the best approximation of the sampling distribution of \widehat{p} each distribution uses the same scale?