STATISTICAL 4.11. Which of the following continuous distributions is symmetrical and unskewed over its typical operating range? a. Normal b. Weibull c. Lognormal d. Exponential 4.12. The means of large samples from a population with finite variance tend to be normally distributed around the population mean. This statement is true according to which of the following theorems? a. Central limit b. Camp-Meidel c. Tchebysheff's d. Least squares 4.13. If f(t), R(t), and h(t) denote the failure time density function, reliability function, and hazard- rate function of a device, which one of the following expressions is true? a. R(t)=exp[-h(s)ds] dt b. h(t)=-(hR(t)] C. f(t)=h(t) R(1) d. h(t)= R(s)ds 4.14. A new refrigerator has a probability of working correctly when it is first plugged in of 0.985. The probability that it will be delivered to the person's home with no dents is 0.947. What is the probability that it will arrive with no damage, and will work the first time? a. 0.932 b. 0.933 c. 0.985 d. 0.999 4.15. A process is in control at X-double bar = 100, R- bar = 7.3 with n = 4. If the process level shifts to 101.5, with the same R-bar, what is the probability that the next X-bar point will fall outside the old control limits? 4.16. 4.17. 4.18. A certain equipment has a MTBF of m = 300 hours. Assuming an exponential distribution of time to failure, what is the maximum time of allowable operation if a reliability of 0.999 is required? a. 30 hours b. 0.3 hours c. 300 hours d. 0.003 hours Which principle underlies the effectiveness of reliability control charting? a. The samples are randomly selected b. The samples are heterogeneous c. The process shows design immaturity d. For reliability applications, the failure rate is erratic A plastics plant operates 8 extruders producing plastic film. Production volume requirements cannot be met if fewer than 6 extruders are operating. There is a 0.30 probability that a machine stopping malfunction will occur. What is the probability that at least 6 extruders can remain operating throughout the day? a. 0.5783 b. 0.4482 c. 0.5518 d. 0.8059 4.19. The sample size needed for hypothesis testing: a. Depends upon the proportion rate b. Can be determined c. Requires a known censor point d. Indicates that a confidence level and reliability must be provided 4.20. In 1000 trials, independent, with the same probability of failure at each trial, 50 failures were observed. Upper and lower 90% (symmetrical 80%) confidence limits on the reliability are: a. 0.96 -0.94 b. 0.980.92 c. 0.99-0.96 d. 1.00 -0.95