4. For a certain type of computer chip, the proportion of chips that are defective is...

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4. For a certain type of computer chip, the proportion of chips that are defective is 0.10. A computer manufacturer receives a shipment of 200 chips. a. Is it appropriate to use the normal distribution to find probabilities for p? b. What is the probability that the proportion of defective chips in the shipment is between 0.08 and 0.15? c. Would it be unusual for the proportion of defective ships to be less than 0.075? 5. In the 2012 U.S. presidential election, 51% of voters voted for Barack Obama. If a sample of 75 voters were polled, a. Is it appropriate to use the normal distribution to find probabilities for p? b. would it be unusual if less than 40% of them had voted for Barack Obama? SECTION 7.6: ASSESSING NORMALITY ASSESSING NORMALITY There are three important ideas to remember when assessing normality: trying to determine whether the population is exactly 1. We are 2. Assessing normality is more important for than for large samples. We will reject the assumption that a population is approximately normal if a sample has any of the following features: 1. The sample contains an 2. The sample exhibits a large degree of 3. The sample has more than distinct mode. 4. If the sample has none of the preceding features, we will treat the population as being DOT PLOT 1. At a recent health fair, several hundred people had their pulse rates measured. A simple random sample of six records was drawn, and the pulse rates, in beats per minute, were 68 71 79 98 67 75 Is it reasonable to treat this as a sample from an approximately normal population? Explain. BoxPlots 2. A recycler determines the amount of recycled newspaper, in cubic feet, collected each week. Following are the results for a sample of 18 weeks. 2129 2853 2530 2054 2075 2011 2162 2285 2668 3194 4834 2469 2380 2567 4117 2337 3179 3157 Is it reasonable to treat this as a sample from an approximately normal population? Explain. Histrograms 3. A shoe manufacturer is testing a new type of leather sole. A simple random sample of 22 people wore shoes with the new sole for a period of four months. The amount of wear on the right shoe was measured for each person. The results, in thousandths of an inch, were 24.1 4.6 2.2 11.8 2.7 4.5 4.1 6.1 4.1 13.9 33.6 2.4 36.2 16.8 5.4 6.3 22.6 29.1 12.2 4.6 15.8 7.7 Is it reasonable to treat this as a sample from an approximately normal population? Explain. STEM-AND-LEAF 4. A psychologist measures the time it takes for each of 20 rats to run a maze. The times, 54 48 49 in seconds, are 54 63 54 66 32 45 52 52 53 41 41 37 56 56 45 48 43 Construct a stem-and-leaf plot for these data. Is it reasonable to treat this as a random sample from an approximately normal population? NORMAL QUANTILE PLOT 5. A placement exam is given to each entering freshman at a large university. A simple random sample of 20 exam scores is drawn, with the following results. 61 60 60 68 63 63 94 66 65 98 61 71 74 63 66 61 61 65 72 85 Construct a normal probability plot using technology. Is the distribution of exam scores approximately normal? 4. For a certain type of computer chip, the proportion of chips that are defective is 0.10. A computer manufacturer receives a shipment of 200 chips. a. Is it appropriate to use the normal distribution to find probabilities for p? b. What is the probability that the proportion of defective chips in the shipment is between 0.08 and 0.15? c. Would it be unusual for the proportion of defective ships to be less than 0.075? 5. In the 2012 U.S. presidential election, 51% of voters voted for Barack Obama. If a sample of 75 voters were polled, a. Is it appropriate to use the normal distribution to find probabilities for p? b. would it be unusual if less than 40% of them had voted for Barack Obama? SECTION 7.6: ASSESSING NORMALITY ASSESSING NORMALITY There are three important ideas to remember when assessing normality: trying to determine whether the population is exactly 1. We are 2. Assessing normality is more important for than for large samples. We will reject the assumption that a population is approximately normal if a sample has any of the following features: 1. The sample contains an 2. The sample exhibits a large degree of 3. The sample has more than distinct mode. 4. If the sample has none of the preceding features, we will treat the population as being DOT PLOT 1. At a recent health fair, several hundred people had their pulse rates measured. A simple random sample of six records was drawn, and the pulse rates, in beats per minute, were 68 71 79 98 67 75 Is it reasonable to treat this as a sample from an approximately normal population? Explain. BoxPlots 2. A recycler determines the amount of recycled newspaper, in cubic feet, collected each week. Following are the results for a sample of 18 weeks. 2129 2853 2530 2054 2075 2011 2162 2285 2668 3194 4834 2469 2380 2567 4117 2337 3179 3157 Is it reasonable to treat this as a sample from an approximately normal population? Explain. Histrograms 3. A shoe manufacturer is testing a new type of leather sole. A simple random sample of 22 people wore shoes with the new sole for a period of four months. The amount of wear on the right shoe was measured for each person. The results, in thousandths of an inch, were 24.1 4.6 2.2 11.8 2.7 4.5 4.1 6.1 4.1 13.9 33.6 2.4 36.2 16.8 5.4 6.3 22.6 29.1 12.2 4.6 15.8 7.7 Is it reasonable to treat this as a sample from an approximately normal population? Explain. STEM-AND-LEAF 4. A psychologist measures the time it takes for each of 20 rats to run a maze. The times, 54 48 49 in seconds, are 54 63 54 66 32 45 52 52 53 41 41 37 56 56 45 48 43 Construct a stem-and-leaf plot for these data. Is it reasonable to treat this as a random sample from an approximately normal population? NORMAL QUANTILE PLOT 5. A placement exam is given to each entering freshman at a large university. A simple random sample of 20 exam scores is drawn, with the following results. 61 60 60 68 63 63 94 66 65 98 61 71 74 63 66 61 61 65 72 85 Construct a normal probability plot using technology. Is the distribution of exam scores approximately normal?