## Related questions with answers

Unfortunately, robbery is an all-too-frequent crime. Bank robberies tend to be the most lucrative for criminals. In most cases banks do not report the size of the loss. However, several researchers were able to gain access to bank robberies in England. Here are the variables recorded:

Bank raid successful from the point of view of the robbers (2 = yes and 1 = no)

Amount stolen (for successful raids only)

Number of bank staff present

Number of customers present.

If these data can be considered a random sample of British bank robberies estimate with 95% confidence the following parameters. Proportion of all bank robberies that are successful

Solution

VerifiedRecall that if the parameter of interest is the proportion, and the sample size is large, we can use the $z$ - test to approximate the confidence interval. The formula for the confidence interval for $\hat{p}$ is

$\hat{p} \pm z_{\alpha/2} \sqrt\dfrac{\hat{p}(1-\hat{p})}{n}$

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