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 575 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 -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 0.06 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 -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.

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.

(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.)

Answer 1

a)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.100
sample size       =n=	575
std error of proportion=σp=√(p*(1-p)/n)=	0.0125

2nd curve is correct with description of
"

• 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.

b)

probability =P(0.070.9836

c)

probability =P(0.0850.7698