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#### ex02_fall08

Course: STAT 303, Fall 2008

School: Texas A&M

Word Count: 1390

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on Based past experience, an architect has determined the probability mass function for the number of times a drawing must be examined by a client before it is accepted. Let the random variable X = the number of times a drawing must be examined by a client before it is accepted. The distribution of X is shown below: Value of X Probability 1 0.1 2 0.2 3 0.3 4 0.2 5 0.2 1. What is the average number of times a...

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on Based past experience, an architect has determined the probability mass function for the number of times a drawing must be examined by a client before it is accepted. Let the random variable X = the number of times a drawing must be examined by a client before it is accepted. The distribution of X is shown below: Value of X Probability 1 0.1 2 0.2 3 0.3 4 0.2 5 0.2 1. What is the average number of times a drawing must be examined by a client before it is accepted? 2. Mr. Klein is one of the clients of this architect. Mr. Klein has already inspected his drawing twice. What is the probability that he will accept the drawing after the next examination (= the third time)? A. 0.3 B. 0.7 C. 0.3570 D. 0.4286 E. Cannot tell from the given information If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probabilities for the color of a randomly chosen M&M: Color Probability Brown 0.3 Red 0.3 Yellow ? Green 0.1 Orange 0.1 Blue 0.1 3. If you select two M&M's and the colors are independent, then what is the probability that both are the same color? A. 0.01 B. 0.09 C. 0.22 D. 0.25 E. Cannot tell from given information 4. Suppose we have two independent random variables X and Y. Which of the following statements about X and Y is/are FALSE? ____The mean of X + Y is the sum of their means. ____The variance of X+Y is the sum of their variances ____The correlation between X and Y is zero. ____The variance of the difference X Y is the difference of their variances (should be sum). ____The mean of the difference X Y is the difference of their means. 5. College basketball has two superstars that nobody can seem to stop this year. Player A averages 39 points a game with a standard deviation of 5 for his university while player B averages 36 points a game with a standard deviation of 3 for his. The player's points are determined to be independent and normally distributed. What is the probability that both of them score less than 20 points on the same night? Hint: We want the P(A < 20 AND B < 20) with A ~ N(39,52) and B ~ N(36,32). A. 0.0228 B. 0.0008 C. 0.0587 D. 0.0359 E. None of the above. 6. Which statement agrees with P(p90 0.20) for p90 ~ N(0.33, 0.0712)? A. What sample proportion is the upper 20% of this population with mean 0.33 and standard deviation 0.071? B. How likely are you to get a sample proportion of 20% or more if you take a sample of 90 from a population with mean 33% and standard deviation 7.1%? C. How likely are you to get 20% or more if you sample a population of 90? D. How likely are you to get a probability of 0.20 if you sample a population with mean 0.33 and standard deviation 0.071? E. Math doesn't equate to words. 7. Which of these situations can use the normal distribution? (Check all that apply) _____The data is not normal, but n > 10 _____The sample is randomly selected _____When p > 10 and (1-p) > 10 _____We are only interested in one measurement, not the sample mean _____The data for proportion is not normal, but n*p > 30>10 and n*(1-p) > 30>10 _____The data is know to be normally distributed, but n < 10 _____The sample mean is large and the standard deviation is small 8. A college basketball player is known to make 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that he makes at least 90 attempts? A. 0.0062 B. 0.2643 C. 0.72 D. 0.90 E. None of the above. 9. Alice is a Political Science major that is interested in the public opinions about the economy. She wants to sample 30 people to find a 95% confidence interval for the proportion of people in the US that believe the economy is the number one issue in the upcoming election. What is the sampling distribution of the sample proportion, p30, if the true population proportion is 0.98 (98%)? 10. You are planning a trip to Spain and want to know what type of clothes you should pack for the trip. A local website for the place you are traveling shows that the temperatures for the days you will there be are normally distributed with a mean of 34C with a standard deviation of 6C. Unfortunately, you are unfamiliar with the Celsius scale and only know that 9 Temp ( F ) = Temp(C ) + 32 and you want to know if you should pack warmer clothes. What is 5 the probability that the temperature will be below 70F? 11. Which of these statements is/are FALSE? ____The distribution of the sample mean is always normal with mean equal to the population mean and standard deviation equal to the standard deviation of the population divided by n. _____Two events A and B are independent if and only if P(A and B) = P(A) * P(B). _____A p-value is the probability of obtaining an estimate as extreme or even more extreme that the one observed. _____Type I errors are equivalent to the significance level, . _____Power is negatively correlated with Type I errors. _____Type II errors are equivalent to Power. Central Middle School has calculated a 95% confidence interval for the mean height ( ) of 11year-old boys at their school and found it to be 56 2 inches. 12. Determine whether each of the following statements is true or false. ____There is a 95% probability that is between 54 and 58. ____There is a 95% probability that the true mean is 56, and there is a 95% chance that the true margin of error is 2. ____If we took many additional random samples of the same size and from each computed a 95% confidence interval for , approximately 95% of these intervals would contain . ____If we took many additional random samples of the same size and from each computed a 95% confidence interval for , approximately 95% of the time would fall between 54 and 58. ____If we took many additional random samples of the same size and from each computed a 95% confidence interval for , approximately 95% of the time X would fall between 54 and 58. 13. Which of the following could be the 90% confidence interval based on the same data? A. 56 1 B. 56 2 C. 56 3 D. 56 2.5 E. Without knowing the sample size, any of the above answers could be the 90% confidence interval. 14. Which of the following statements is correct? A. An extremely small p-value indicates that the actual data differs markedly from that expected if the null hypothesis were true. B. The p-value measures the probability that the null hypothesis is true. C. The p-value measures the probability of making a Type II error. D. The larger the p-value, the stronger the evidence against the null hypothesis. E. None of the above statements are true. The distribution of GPA scores is known to be l...

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