mean of 38000 miles and a standard deviation of 2600 miles. If it guarantees that tires last at least 32540 ​miles, what % of tires will live up to guarantee?

Question

PLEASE GIVE THE PERCENT OF THE Z-SCORE. ROUND TO TWO DECIMAL PLACES. 

Answer 1

z = (x-μ)/σ

• z = z score
• x = data point = 32,540
• μ = mean of the data set = 38,000
• σ = standard deviation of the data set = 2600

 

Compute the z score using the above formula and data.  Then look up the percentile on a z-score table (http://www.z-table.com/).  That will give you the percent that do NOT live up to the guarantee.  The percent that DO live up to the guarantee is 100% - (z score percentile ·100).