People end up tossing 12% of what they buy at the grocery store ( Reader\'s Dige

Question

People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. Use z-table.

Show the sampling distribution of (), the proportion of groceries thrown out by your sample respondents (to 4 decimals).

SelectCannot assumed to be normally distributedCan assume to be normally distributed because n>=30 and sigma is givenCan assume to be normally distributed because n>100Can assume to be normally distributed because the underlying population is normally distributed and sigma is givenCan assume to be normally distributed because np>=5 and n(1-p)>=5Item 1

p =  

standard error of the proportion (  ) =  

What is the probability that your survey will provide a sample proportion within ±.03 of the population proportion (to 4 decimals)?

What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion (to 4 decimals)?

Explanation / Answer

Can assume to be normally distributed because np>=5 and n(1-p)>=5

p = 0.12
SE = sqrt(0.12 * 0.88/540) = 0.014

0.03/0.014 = 2.1453

P(within +/- 0.03)
= P(-2.1453 < z < 2.1453)
= P(z < 2.1453) - P(z < -2.1453)
= 0.98404 - 0.01596 .. (using standard z table)
= 0.9681

0.015/0.014 = 1.0714
P(within +/- 0.015)
= P(-1.0714 < z < 1.0714)
= P(z < 1.0714) - P(z < -1.0714)
= 0.85801 - 0.14199 .. (using standard z table)
= 0.7160

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