There is an ongoing debate about whether to label genetically engineered (GE) fo

Question

There is an ongoing debate about whether to label genetically engineered (GE) foods. In the United States, many processed foods include at least one GE ingredient, for example, GE soybeans, corn, or canola. Suppose 70% of all Americans believe GE foods should be labeled and a random sample of 500 Americans is selected. Answer part b) using the normal approximation to the binomial distribution. a) Is the normal approximate to the binomial appropriate in this situation? Do part b) no matter what your answer is. b) Find the approximate probability that at least 340 Americans believe GE foods should be labeled. Remember the continuity correction.

Explanation / Answer

p = proportion of americans who believe GE foods should be labeled = 0.7

q = 1 - p =0.3

n = 500

a) Yes it is normal approximate to the binomial distribution .As the data moves to proportion of GE foods.

b) P ( atleast 340 americans believe GE foods should be labeled ) = P ( x > 340 )

n*p = 500 * 0.7 = 350 (mean)

n *q = 500 * 0.3 = 150

n* p *q = 500 * 0.7 * 0.3 = 105 (variance)

Continuity correction factor x > 340 becomes x > 339.5

z =( x - mean ) / sqrt (variance) = (340 - 350 ) / sqrt ( 105) = -0.9759

From z-table , -0.9759 = 0.1660

As we wanr right tail curve = 0.5 + 0.1660 = 0.6660

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