The critical z value which should be used in determining the confidence interval is z=1.29 and the confidence interval is (38.43355,66.82645).
Given sample mean of $52.63 and standard deviation of $22.01.
We have to construct  the confidence interval of 80% for the mean repair cost for the washers.
μ=52.63
σ=22.01
n=4
First we have to find the value of z for the confidence level of 80% from z table and which is 1.29.
Margin of error is the difference between the calculated values and real values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where μ is mean
σ is standard deviation
n is sample size
z is z value for the confidence level
Margin of error=1.29*22.01/[tex]\sqrt{4}[/tex]
=14.19645
Confidence interval =mean ±margin of error
Upper level=mean +margin of error
=52.33+14.19645
=66.82645
Lower level=mean-margin of error
=52.33-14.19645
=38.43355
Hence the confidence interval is (38.43355,66.82645) and the critical value used is z=1.29.
Learn more about confidence interval at https://brainly.com/question/15712887
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