In: Statistics and Probability
You may need to use the appropriate appendix table or technology
to answer this question.
In...
You may need to use the appropriate appendix table or technology
to answer this question.
In 2017, a website reported that only 10% of surplus food is
being recovered in the food-service and restaurant sector, leaving
approximately 1.5 billion meals per year uneaten. Assume this is
the true population proportion and that you plan to take a sample
survey of 535 companies in the food service and restaurant sector
to further investigate their behavior.
(a)
Show the sampling distribution of
p,
the proportion of food recovered by your sample respondents.
A bell-shaped curve is above a horizontal axis labeled p.
- The horizontal axis ranges from about -0.03 to about 0.05.
- The curve enters the viewing window near -0.03 just above the
horizontal axis, curves up to the right, and reaches a maximum near
0.01.
- The curve then curves down and to the right until it leaves the
viewing window at the same height it entered near 0.05.
A bell-shaped curve is above a horizontal axis labeled p.
- The horizontal axis ranges from about 0.06 to about 0.14.
- The curve enters the viewing window near 0.06 just above the
horizontal axis, curves up to the right, and reaches a maximum near
0.10.
- The curve then curves down and to the right until it leaves the
viewing window at the same height it entered near 0.14.
A bell-shaped curve is above a horizontal axis labeled p.
- The horizontal axis ranges from about -2.9 to about 3.1.
- The curve enters the viewing window near -2.9 just above the
horizontal axis, curves up to the right, and reaches a maximum near
0.1.
- The curve then curves down and to the right until it leaves the
viewing window at the same height it entered near 3.1.
A bell-shaped curve is above a horizontal axis labeled p.
- The horizontal axis ranges from about -0.04 to about 0.04.
- The curve enters the viewing window near -0.04 just above the
horizontal axis, curves up to the right, and reaches a maximum near
0.00.
- The curve then curves down and to the right until it leaves the
viewing window at the same height it entered near 0.04.
(b)
What is the probability that your survey will provide a sample
proportion within ±0.03 of the population proportion? (Round your
answer to four decimal places.)
(c)
What is the probability that your survey will provide a sample
proportion within ±0.015 of the population proportion? (Round your
answer to four decimal places.)