Prob and Stats
frequency distribution
How many pieces of data are in each interval.
Based on sample data, newborn males have weights with a mean of 3232.9 g and a standard deviation of 768.7 g. Newborn females have weights with a mean of 3020.4 g and a standard deviation of 514.9 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?
Since the z score for the male is zequals negative 1.99 and the z score for the female is zequals negative 2.56, the female has the weight that is more extreme. (Round to two decimal places.)
Refer to the sample data for polygraph tests shown below. If one of the test subjects is randomly selected, what is the probability that the subject is not lying? Is the result close to the probability of 0.398 for a negative test result? Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) Positive test results 17 45 Negative test results 27 14
The probability that a randomly selected polygraph test subject was not lying is 0.427. (Type an integer or decimal rounded to three decimal places as needed.) Is the result close to the probability, rounded to three decimal places, of 0.398 for a negative test result? Yes, because there is less than a 0.050 absolute difference between the probability of a true response and the probability of a negative test result.
Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general? 41 39 38 31 23 20 18 17 16.5 15.9
The range of the sample data is $ 25.1 million. (Type an integer or a decimal.) The variance of the sample data is 105.02. (Round to two decimal places as needed.) The standard deviation of the sample data is $ 10.25 million. (Round to two decimal places as needed.) Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general? A. No, because the sample is not representative of the whole population. This is the correct answer.B. Yes, because the sample is random. C. No, because there is an outlier in the sample data. D. Yes, because the standard deviation is an unbiased estimator.
In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)equals0.710, where D is directly in person. If someone is randomly selected, what does Upper P left parenthesis Upper D overbar right parenthesis represent, and what is its value?
Upper P left parenthesis Upper D overbar right parenthesisequals 0.290 (Simplify your answer.)
A certain group of women has a 0.81% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
What is the probability that the woman selected does not have red/green color blindness? 0.9919 (Type an integer or a decimal. Do not round.)
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us? 39 6 72 24 78 43 9 99 26 75 81
a. Find the mean. The mean is 50.2. (Type an integer or a decimal rounded to one decimal place as needed.) b. Find the median. The median is 43. (Type an integer or a decimal rounded to one decimal place as needed.) c. Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode(s) is(are) nothing. (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) B. There is no mode. Your answer is correct. d. Find the midrange. The midrange is 52.5. (Type an integer or a decimal rounded to one decimal place as needed.) e. What do the results tell us? A. The mean and median give two different interpretations of the average (or typical) jersey number, while the midrange shows the spread of possible jersey numbers. B. The jersey numbers are nominal data and they do not measure or count anything, so the resulting statistics are meaningless. Your answer is correct.C. Since only 11 of the jersey numbers were in the sample, the statistics cannot give any meaningful results. D. The midrange gives the average (or typical) jersey number, while the mean and median give two different interpretations of the spread of possible jersey numbers.
5 number summary
min, Q1, median, Q3, max
Because the mean is very sensitive to extreme values, it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and delete the top 10% of the values, then calculate the mean of the remaining values. Use the axial loads (pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean. 247 261 268 272 275 278 280 283 283 284 287 288 290 290 294 294 297 299 310 507
Identify any outliers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The outlier(s) is/are 507 pounds. (Type a whole number. Use a comma to separate answers as needed.) Your answer is not correct.B. There are no outliers. The median is 285.5 pounds. (Type an integer or decimal rounded to one decimal place as needed.) The untrimmed mean is 294.4 pounds. (Type an integer or decimal rounded to one decimal place as needed.) The 10% trimmed mean is 285.1 pounds. (Type an integer or decimal rounded to one decimal place as needed.) The 20% trimmed mean is 285.5 pounds. (Type an integer or decimal rounded to one decimal place as needed.) Compare the values. Choose the correct answer below. A. All of the values are close to each other. B. The median, untrimmed mean, and 20% trimmed mean are close to each other. However, the 10% trimmed mean is significantly different from those values. C. The median, untrimmed mean, and 10% trimmed mean are close to each other. However, the 20% trimmed mean is significantly different from those values. D. The untrimmed mean, 10% trimmed mean, and 20% trimmed mean are close to each other. However, the median is significantly different from those values. E. The median, 10% trimmed mean, and 20% trimmed mean are close to each other. However, the untrimmed mean is significantly different from those values.
How to find outliers
Q1 - 1.5(IQR) Q3 + 1.5(IQR)
IQR
Q3-Q1
