factory manufactures a specific component and the average of a sample of 1000 of

Question

factory manufactures a specific component and the average of a sample of 1000 of these components yielded a mean of 5.13 cm and a standard deviation of 0.042 cm. Assume that the length distribution of the components follow a normal distribution and use the sample statistics as indicators of the population mean and standard 4. A deviation to determine (a) the probability that the length of a components is between 5 .10 cm and 5.15 cm and (b) the minimum and maximum lengths for which 90% of the components lie evenly distributed within these boundaries.

Explanation / Answer

a) as we know that z score =(X-mean)/std deviation

therefore P(5.10<X<5.15) =P((5.10-5.13)/0.042<Z<(5.15-5.13)/0.042)=P(-0.7143<Z<0.4762)=0.6830-0.2375

=0.4455

b)

for middle 90% values fall between 5th and 95th percentile for which z score = -/+1.645

therefore mimimum length =mean +z*Std deviation =5.13-1.645*0.042=5.199

maximum length =mean +z*Std deviation =5.13+1.645*0.042=5.061

please revert for any clarification required

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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