A machine at Katz Steel Corporation makes 4-inch-long nails. The probability dis

Question

A machine at Katz Steel Corporation makes 4-inch-long nails. The probability distribution of the lengths of these nails is approximately normal with a mean of 4 inches and a standard deviation of 0.12 inch. The quality control inspector takes a sample of 25 nails once a week and calculates the mean length of these nails. If the mean of this sample is either less than 3.95 inches or greater than 4.05 inches, the inspector concludes that the machine needs an adjustment. What is the probability that based on a sample of 25 nails, the inspector will conclude that the machine needs an adjustment?

Round your answer to 4 decimal places.

Probability =

Explanation / Answer

Mean is 4 and s is 0.12. the standard error for sample of 25 nails is SE=s/sqrt(N)=0.12/sqrt(25)=0.024

We need P(needs adjustment)= 1-P(3.95<x<4.05) or 1-P((3.95-4)/0.024<z<(4.05-4)/0.024) =1-P(-2.08<z<2.08)

which is 1-(2*P(z<2.08)-1) or 2-2*P(z<2.08), from normal distribution table we get 2-2*0.9812 =0.0376

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.