What does a z-score of 3 for a data value x represent?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
1. What does a z-score of 3 for a data value x represent?
2. What does a x score of -1 for data value x represent?
3. Given; Mean= 68.73 s.d.= 9.03 Find
a. what percentage of the scores fall above 50? below 75? between 60 and 79? above 80? between 53 and 67? exactly 73?
4. Find the area of the standard normal distribution between z=-0.67 and z=0.
5. Cheryl has taken two quizzes in her history class. She scored 15 on the second quiz, for which the mean of all scores was 12 and the standard deviation was 2.4. Her score on the second quiz, for which the mean of all scores was 11 and the standard deviation was 2.0 was 14. In comparison to her classmates, did Cheryl do better on the first quiz or the second quiz? Justify your answer.
6. Roland received a score of 70 on a test for which the mean score was 65.5. Roland has learned that the z score for his test is 0.6. What is the standard deviation for this test scores?
7. Use the relative frequency distribution in Table 6.1 to determine the
a. Percent of subscribers who required less than 25 s to download the file
b. Probability that the subscriber chosen at random will require atleast 10 s but less than 30 s to download the file.
8. A vegetable distributor knows that during the month of August, the weights of its tomatoes are
a. What percent of the tomatoes weigh less than 0.76 lb?
b. In a shipment of 6000 tomatoes, how many tomatoes can be expected to weigh more than 0.31 lb?
c. In a shipment of 4500 tomatoes, how many tomatoes can be expected to weigh from 0.31 lb to 0.91 lb?
9. A study shows that the lengths of the careers of professional football players are nearly normally distributed, with mean of 6.1 years and a standard deviation of 1.8 years.
a. What percent of professional footbal players have a career of more than 9 years?
b. If a professional football player is chosen at random, what is the probability that the player will have a career of between 3
10. A consumer grouped tested a sample of 100 light bulbs. It found that the mean life expectance of the bulbs was 842 hours, with a standard deviation of 90. One particular light bulb had a z-score of 1.2. What was the life span of this bulb?
11. On a reading examination given to 900 students, Fe's score of 602 was higher than the scores of 576 of the students who took the examination. What is the percentile for Fe's score?
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