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My name is Ann [436]
3 years ago
13

According to a 2009 Reader's Digest article, people throw away approximately 13% of what they buy at the grocery store. Assume t

his 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 0.16?
Mathematics
1 answer:
OverLord2011 [107]3 years ago
4 0

Answer:

The probability that the sample proportion exceeds 0.16 is 0.2061.

Step-by-step explanation:

We are given that according to a 2009 Reader's Digest article, people throw away approximately 13% of what they buy at the grocery store.

You plan to randomly survey 101 grocery shoppers to investigate their behavior.

Let \hat p = sample proportion

The z-score probability distribution for the sample proportion is given by;

                               Z  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample population = 0.16

           n = sample of grocery shoppers = 101

Now, the probability that the sample proportion exceeds 0.16 is given by = P(\hat p > 0.16)

  P(\hat p > 0.16) = P( \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } > \frac{0.16-0.13}{\sqrt{\frac{0.16(1-0.16)}{101} } } ) = P(Z > 0.82) = 1 - P(Z \leq 0.82)

                                                               = 1 - 0.7939 = <u>0.2061</u>

The above probability is calculated by looking at the value of x = 0.82 in the z table which has an area of 0.7939.

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