1.According to a 2009 Reader\'s Digest article, people throw away approximately

Question

1.According to a 2009 Reader's Digest article, people throw away approximately 14% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 92 grocery shoppers to investigate their behavior. What is the probability that the sample proportion is between 0.05 and 0.14?

2.Based on historical data, your manager believes that 39% of the company's orders come from first-time customers. A random sample of 90 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.25 and 0.46?

3.A population of values has a normal distribution with =185.9=185.9 and =37.3=37.3. You intend to draw a random sample of size n=166n=166.

What is the mean of the distribution of sample means?
¯x=x¯=  (Enter your answer as a number accurate to 4 decimal places.)

What is the standard deviation of the distribution of sample means?
(Report answer accurate to 4 decimal places.)
¯x=x¯=

Explanation / Answer

1) here p=0.14

n=92 ; std error =(p(1-p)/n)1/2 =0.036

therefore P(0.05<X<0.014)=P((0.05-0.14)/0.036<Z<(0.14-0.14)/0.036)=P(-2.4878<Z<0)=0.5-0.0064 =0.4936

2)

here p=0.39

n=90 ; std error =(p(1-p)/n)1/2 =0.0514

therefore P(0.25<X<0.46)=P((0.25-0.39)/0.0514<Z<(0.46-0.39)/0.0514)=P(-2.7230<Z<1.3615)=0.9133-0.0032

=0.9101

3)

mean of the distribution of sample means=185.9

standard deviation of the distribution of sample means =std deviation/(n)1/2 =2.8950

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