Florida International University

Statistics I - STA 3111

Ms. Laura Reisert Instructor

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Chapter 5 - Review Problem

1. A machine used to regulate the amount of dye dispensed for mixing shades of paint can be set so that it discharges an average of mu milliliters of dye per can of paint. The amount of dye discharged is known to have a normal distribution with a standard deviation of .6 milliliter. If more than 9 milliliters of dye are discharged when making a particular shade of gray paint, the shade is unacceptable. Determine the setting for mu so that only 2 percent of the cans of paint will be unacceptable.
2. A physical fitness association is including the mile run in their secondary school fitness test for boys. The time for this event for boys is approximately normally distributed with a mean of 428 seconds and a standard deviation of 30 seconds. If the association wants to designate the fastest 5% as "excellent", what time should the association set for this criterion?
3. The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 485 and the standard deviation was 88. If the board wants set the passing score so that only the best 20% of all applicants pass, what is the passing score? Assume the scores are normally distributed.
4. The distribution of the demand (in number of units per unit time) for a product can often be approximated by a normal probability distribution. For example, a bakery has determined that the number of loaves of its whole wheat bread demanded daily has a normal distribution with a mean of 5800 loaves and a standard deviation of 250 loaves. Based on cost considerations the company has decided that its best strategy is to produce a sufficient number of loaves so that it will fully supply demand on 97% of all days.

• How many loaves of bread should the company produce?
• Based on the production in the previous part, on what percentage of days will the company be left with more than 400 loaves of unsold bread?

5. To check the effectiveness of a new production process, 1000 photoflash devices were randomly selected from a large number that had been produced. If the process actually produces 8% defectives, what is the probability that more than 75 defectives appear in the sample of 1000?

6. This past year, an elementary school began using a new method to teach arithmetic to first graders. A standardized test, administered at the end of the end of the year, was used to measure the effectiveness of the new method. The distribution of past scores on the standardized test produced a mean of 71 with a standard deviation of 16. If the new method is no different from the old method, what is the probability that the mean score of a random sample of 60 students will be greater than 75?