Two different random samples were collected from the same po…

Two different random samples were collected from the same population. Each sample has a different sample size. Confidence intervals (two-sided) were constructed on the population mean, one for each sample. The first sample had 60 observations, had a sample mean of 18.2, and a sample standard deviation of 3.5. A 90% confidence interval was constructed. The second sample had 35 observations, had a sample mean of 25.9, and a sample standard deviation of 4.9. A 95% confidence interval was constructed. How do the widths of the two confidence intervals compare to each other? 

A certain facility produces drill bits which are made of eit…

A certain facility produces drill bits which are made of either steel, cobalt, or diamond. Suppose that 75% of the drill bits are steel, 20% are cobalt, and 5% are diamond. Further, suppose that 10% of the steel drill bits fail, 5% of the cobalt drill bits fail, and 1% of the diamond drill bits fail. What is the probability that the drill bit is cobalt and fails?   

A manufacturing facility constructs airplanes with a mean of…

A manufacturing facility constructs airplanes with a mean of 50 tons and a variance of 400. What is the smallest probability that an airplane’s weight will be between 20 tons and 80 tons? Note that we are not assuming normality.  [Hint: Use Chebyshev’s theorem.]