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Directions: Try to take the exam as if it were an actual test. When you finish, click the problems one-by-one to check your answers. There is a view answer link to just see the text solution, but if you got the problem wrong, you should watch the included video as well.

1. An important bolt is manufactured for use in high speed trains at a plant in Germany. The lengths of the manufactured bolts are normally distributed with a mean of 20.0 cm and a standard deviation of 0.042 cm. Because of variation due to operator error and other more subtle issues, some bolts are made too short and others are too long to be used safely. Bolts that come off the production line shorter than 19.88 cm or longer than 20.12 cm cannot be used. What percentage of bolts will be unusable?

2. International flights allow checked luggage to weigh up to 22 kg without additional charge. However, if you go over, the penalty can be steep. If baggage weights are normally distributed with a mean of 18.8 kg and a standard deviation of 1.9 kg, what percentage of passengers will be forced to pay the penalty or to remove items from their luggage?

3. Measurement error is common especially when the measurements are made by human researchers. If the measurement errors for body fat measurements are normally distributed with an average of 4 percentage points and a standard deviation of 0.53 points, what is the probability that a particular body fat reading taken by a researcher will be in error by at most 3 percent?

4. The diameters of sausage produced by a certain brand of sausage maker are normally distributed with a mean of 2.0 inches and a standard deviation of 0.05 inches. What is the probability that the diameter of a randomly selected sausage is between 1.92 and 2.09 inches.

5. The weights of TI-83 calculators are normally distributed with a mean of 0.6 lbs and a standard deviation of 0.01 lbs. What is the probability that a randomly selected TI-83 calculator weighs exactly 0.62 lbs?

6. For young poplar trees aged 18-24 months old, their heights are normally distributed with a mean of 91.44 cm and a standard deviation of 13.1 cm. If samples of 49 young poplar trees are selected at random from the population, would the average heights of those samples be as varied as the individual measurements taken for each tree?

7. For young poplar trees aged 18-24 months old, their heights are normally distributed with a mean of 91.44 cm and a standard deviation of 13.1 cm. If samples of 49 young poplar trees are selected at random from the population, Find the standard error of the population of sample means.

8. If the average score for my second exam on probability is 75 points with a standard deviation of 12.5 points, what is the probability that a random selection of 55 students has an average exam score above 80 points?

9. The diameters of sausage produced by a certain brand of sausage maker are normally distributed with a mean of 2.0 inches and a standard deviation of 0.05 inches. Find the mean of the population of sample means when samples of size 15 are randomly selected from the population.

10. If y is a point estimator for λ and the E(y) = λ + 7, is y a biased estimator of λ or an unbiased estimator of λ?

11. Find P( Z < 1.07 )

12. Male weights are normally distributed with a mean of 172 lbs and a standard deviation of 29 lbs. Find P35, which is the weight separating the bottom 35% from the top 65%.

13. If the scores for my third exam in STA 2122 are normally distributed with an average score of 78 points with a standard deviation of 12.3 points, find P75, which is the score separating the bottom 75% from the top 25%.

14. Find P( -2.13 < Z < -1.17 )

15. Find P( 0 < Z < 1.91 )

16. Find P( -3.02 < Z < 0.52)

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