You may need to use the appropriateappendix tableortechnologyto answer this question.The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is

p= 0.17

and a sample of600householdswill be selected from the population.(a)Show the sampling distribution of

p,

the sample proportion of households spending more than $100 per week on groceries.

A bell-shaped curve is above a horizontal axis labeledp.

• In order of left to right, the ticks on the horizontal axis are labeled:0.015, 0, 0.015, 0.03, 0.045.
• The curve enters the viewing window near0.015 just above the horizontal axis and travels up to the right to a maximum near 0.015.
• After reaching the maximum, the curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.045.

A bell-shaped curve is above a horizontal axis labeledp.

• In order of left to right, the ticks on the horizontal axis are labeled: 0.14, 0.155, 0.17, 0.185, 0.2.
• The curve enters the viewing window near 0.14 just above the horizontal axis and travels up to the right to a maximum near 0.17.
• After reaching the maximum, the curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.2.

A bell-shaped curve is above a horizontal axis labeledp.

• In order of left to right, the ticks on the horizontal axis are labeled:0.03,0.015, 0, 0.015, 0.03.
• The curve enters the viewing window near0.03 just above the horizontal axis and travels up to the right to a maximum near 0.
• After reaching the maximum, the curve then travels down and to the right until it leaves the viewing window at the same height it entered near 0.03.

A bell-shaped curve is above a horizontal axis labeledp.

• In order of left to right, the ticks on the horizontal axis are labeled: -1.83, -0.83, 0.17, 1.17, 2.17.
• The curve enters the viewing window near -1.83 just above the horizontal axis and travels up to the right to a maximum near 0.17.
• After reaching the maximum, the curve then travels down and to the right until it leaves the viewing window at the same height it entered near 2.17.

(b)What is the probability that the sample proportion will be within0.02 of the population proportion? (Round your answer to four decimal places.)

(c)Answer part (b) for a sample of1,200households. (Round your answer to four decimal places.)