8.21 A soft-drink machine is regulated so that the amount of drink dispensed averages 240 milliliters with a standard deviation of 15 milliliters. Periodically, the machine is checked by taking a sample of 40 drinks and computing the average content. If the mean of the 40 drinks is a value within the interval x ± 208, the machine is thought to be operating satisfactorily; oth- erwise, adjustments are made. In Section 8.3, the com- pany official found the mean of 40 drinks to be = 236 milliliters and concluded that the machine needed no adjustment. Was this a reasonable decision?

The time to finish a race in minutes is lognormally distributed. The mean of the log (base 10) transformed time is 2.38 and the standard deviation is 0.4. a. What is the time by which 80% of the runners will finish the race? b. What percent of runners will finish the race between 60 and 100 minutes?

A population has a mean of u = 50 and a standard deviation of a = 10. If 3 points were added to every score in the population, what would be the new values for the mean and standard deviation? O The new mean is u = 47, and the new standard deviation is a = 13. The new mean is u = 47, and the standard deviation is still a = 10. O The new mean is u = 53, and the standard deviation is still o = 10. O The mean is still u = 50, and the new standard deviation is a = 13. If every score in the population were multiplied by 2, what would be the new values for the mean and standard deviation? The new mean is µ = 100, and the new standard deviation is still a = 10. The new mean is u = 52, and the new standard deviation is o = 20. The new mean is u = 100, and the new standard deviation is a = 20. The mean is still u = 50, and the new standard deviation is o = 20.

A population of unknown shape has a mean of 1900 and a standard deviation of 120 A) Find the minimum proportion of observations in the population that are in the range 1540 to 2260 B) Determine the maximum proportion of observation that are above 2140