Question 1192336
**1. Determine the z-score:**

* Find the z-score that corresponds to a 94% confidence level. This means we want to find the z-score that leaves 3% in each tail of the standard normal distribution.
* Using a standard normal distribution table or calculator, we find that z ≈ 1.8808.

**2. Estimate the proportion of defective washing machines:**

* Since we don't have any prior information about the proportion of defective washing machines, we'll use the most conservative estimate: p = 0.5. This will give us the largest sample size needed.

**3. Calculate the sample size:**

* Use the following formula for determining the sample size needed for estimating a population proportion:

   n = (z² * p * (1 - p)) / E² 

   where:
      * n is the sample size
      * z is the z-score 
      * p is the estimated proportion of defective washing machines
      * E is the desired margin of error (0.015 in this case)

* Plug in the values:

   n = (1.8808² * 0.5 * (1 - 0.5)) / 0.015²
   n ≈ 7861.16

* **Round up:** Since we can't have a fraction of a washing machine, we round up to the nearest whole number.

**Therefore, the manufacturer should check a sample of 7862 washing machines to be 94% confident that the true proportion of defective washing machines is estimated to within 0.015.**