Questions from Engineering Statistics

Q: A company pays its employees an average wage of $15.

A company pays its employees an average wage of $15.90 an hour with a standard deviation of $1.50. If the wages are approximately normally distributed and paid to the nearest cent, (a) what percentage...

Q: Suppose X follows a continuous uniform distribution from 1 to 5.

Suppose X follows a continuous uniform distribution from 1 to 5. Determine the conditional probability P(X >2.5 | X ≤ 4).

Q: The weights of a large number of miniature poodles are approximately normally

The weights of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 kilogram. If measurements are recorded to the neare...

Q: Many cardiac patients wear an implanted pacemaker to control their heartbeat.

Many cardiac patients wear an implanted pacemaker to control their heartbeat. A plastic connector module mounts on the top of the pacemaker. Assuming a standard deviation of 0.0015 inch and an approxi...

Q: Consider S’2, the estimator of σ2, from Exercise 9.

Consider S’2, the estimator of σ2, from Exercise 9.29. Analysts often use S’2 rather than dividing the degrees of freedom in the sample. (a) What is th...

Q: If X is a binomial random variable, show that (

If X is a binomial random variable, show that (a) ^P = X/n is an unbiased estimator of p; (b) P’ = X+√n/2 / n+√n is a biased estimator of p.

Q: Show that the estimator P’ of Exercise 9.31(b

Show that the estimator P’ of Exercise 9.31(b) becomes unbiased as n→∞.

Q: Compare S2 and S ‘2 (see Exercise 9.29

Compare S2 and S ‘2 (see Exercise 9.29), the two estimators of σ2, to determine which is more efficient. Assume these estimators are found using X1,X2, . . . , Xn, independent random variables from n(...

Q: Consider Exercise 9.33. Use the MSE discussed in Exercise

Consider Exercise 9.33. Use the MSE discussed in Exercise 9.28 to determine which estimator is more efficient. Write out MSE(S2) / MSE(S’2).

Q: A random sample of size n1 = 25, taken from a

A random sample of size n1 = 25, taken from a normal population with a standard deviation σ1 = 5, has a mean ¯x1 = 80. A second random sample of size n2 = 36, taken from a different normal population...