Question 1198701
**1. Determine the Z-score for the desired confidence level:**

* For a 90% confidence level, the area in each tail of the standard normal distribution is (100% - 90%) / 2 = 5%.
* Find the z-score that corresponds to an area of 0.05 in the right tail of the standard normal distribution. 
    * Using a standard normal table or calculator, you'll find that z = 1.645.

**2. Calculate the Margin of Error (E)**

* E = Z * (σ / √n) 
    * where:
        * E = desired margin of error (3 minutes)
        * Z = z-score for the desired confidence level (1.645)
        * σ = population standard deviation (28 minutes)
        * n = sample size

**3. Rearrange the formula to solve for n:**

* n = (Z * σ / E)²

**4. Substitute the values and calculate the sample size:**

* n = (1.645 * 28 / 3)² 
* n ≈ 182.34

**5. Round up to the nearest whole number:**

* Since we need a whole number of samples, round up n to 183.

**Therefore, the consultant must collect a minimum sample size of 183 shopping times to be 90% confident that her estimate of the mean shopping time is within 3 minutes of the true population mean.**