Question

According to a 2009 Reader's Digest article, people throw away approximately 10% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 101 grocery shoppers to investigate their behavior. What is the probability that the sample proportion exceeds 0.2?

Answer =  (Enter your answer as a number accurate to 4 decimal places.)

Answer 1

Solution-

According to question,

People throw away approximately 10% of what they buy at the grocery store.

So, Probability of throwing the grocery = 0.1

Random survey of number grocer shoppers to investigate their behavior=101

So, n=101

We know that for the population proportion, test statistics is

Here, p^ =0.2

So, on putting the values,we get

Or

Or

Or

Or

Now, from the standard normal distribution table

P(z <3.35)==0.9996

Now, the probability that the sample proportion exceeds 0.2

P(p > 0.2)

= P(z >3.35)

= 1- P(z <3.35)

= 1- 0.9996

=0.0004

Hence, Probability that the sample proportion exceeds 0.2 is 0.0004