The Parks Mall wishes to determine the number of its shoppers who come to the mall more than once a week. A random survey of 120 shoppers finds that 45 of them come to the mall more than once a week. If an estimated 1,000 shoppers visit the mall in one day, how many are predicted to return during the same week?

Question

27-12-2023
Mathematics

College

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The Parks Mall wishes to determine the number of its shoppers who come to the mall more than once a week. A random survey of 120 shoppers finds that 45 of them come to the mall more than once a week. If an estimated 1,000 shoppers visit the mall in one day, how many are predicted to return during the same week?

Answer :

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Sashacork Sashacork · Answer 1 · 2023-10-23T08:52:46-04:00

We can predict that 375 shoppers are likely to return to the mall during the same week.

How to estimate the number of shoppers?

To estimate the number of shoppers who are predicted to return during the same week, we need to use the proportion of shoppers who come to the mall more than once a week in the random survey as an estimate for the proportion of all shoppers who come to the mall more than once a week.

From the random survey, we have:

Number of shoppers surveyed (n) = 120

Number of shoppers who come to the mall more than once a week in the survey (x) = 45

So the proportion of shoppers who come to the mall more than once a week in the survey is p-hat = x/n = 45/120 = 0.375

We can use this proportion to estimate the number of shoppers who come to the mall more than once a week in the population of 1,000 shoppers who visit the mall in one day,

predicted number of shoppers who come to the mall more than once a week = p-hat × population size

= 0.375 × 1000

= 375

Therefore, we can predict that 375 shoppers are likely to return to the mall during the same week.

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