Problem

A labor rights group wants to determine the mean salary of app-based drivers. If she knows that the standard deviation is $\$ 3.9$, how many drivers should she consider surveying to be $90 \%$ sure of knowing the mean will be within $\pm \$ 0.76$ ? 72 9 44 39 1084

Solution

Step 1 :This problem is about determining the sample size for estimating a population mean with a known standard deviation. The formula for the sample size n is given by: \(n = (Z*σ/E)^2\)

Step 2 :In this formula, Z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and E is the desired margin of error.

Step 3 :For this problem, the desired confidence level is 90%, which corresponds to a z-score of 1.645. The standard deviation σ is given as $3.9, and the desired margin of error E is $0.76.

Step 4 :We can substitute these values into the formula to find the required sample size: \(n = (1.645*3.9/0.76)^2\)

Step 5 :Calculating this gives a sample size of 72.

Step 6 :Final Answer: The labor rights group should consider surveying \(\boxed{72}\) drivers to be 90% sure of knowing the mean will be within $\pm$ $0.76.

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Source: https://solvelyapp.com/problems/7498/

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