Question

According to Crown ATM Network, the mean ATM withdrawal is $67. Assume thatthe standard deviation for withdrawals is $35. What cutoff sample mean ATMwithdrawal would be required to put a sample of size 50 in the top 5% of samplemeans? Round to the nearest cent.

Answer 1

The formula for the z-score is as follows:

`z=(x-\mu)/(\sigma)`

where z is the score, μ is the mean, and σ is the standard deviation.

To obtain the z-score, which indicates that the score is above the 95% of the sample, check the z-score table and look for 0.9500.

Since 0.95 is in between 0.9495 and 0.9505, the z-score must be 1.645.

Thus, we have the following:

`\begin{gathered} 1.645=(x-67)/(35) \\ 35(1.645)=x-67 \\ 57.575=x-67 \\ 57.575+67=x \\ 124.575=x \\ x\approx124.58 \end{gathered}`