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According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 25 minutes. a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the figures be? 394 to 444 b. If the distribution of time spent on the job is approximately bell shaped, between what two times would 95% of the figures be? 369 to 469 c. If the distribution of time spent on the job is approximately bell shaped, between what two times would 99.7% of the figures be? 344 to 494 d. If the shape of the distribution of times is unknown, approximately what percentage of the times would be between 358 and 480 minutes? 98.1 % (Round the intermediate values to 3 decimal places. Round your answer to 1 decimal place.) e. Suppose a worker spent 400 minutes on the job. What would that worker's z score be, and what would it tell the researcher? z score = -0.760 (Round your answer to 3 decimal places.) This worker is in the lower half of workers but within one standard deviation of the mean.Financial analysts like to use the standard deviation as a measure of risk for a stock. The greater the deviation in a stock price over time, the more risky it is to invest in the stock. However, the average prices of some stocks are considerably higher than the average price of others, allowing for the potential of a greater standard deviation of price. For example, a standard deviation of $5.00 on a $10.00 stock is considerably different from a $5.00 standard deviation on a $40.00 stock. In this situation, a coefficient of variation might provide insight into risk. Suppose stock X costs an average of $36.00 per share and showed a standard deviation of $3.10 for the past 60 days. Suppose stock Y costs an average of $84.00 per share and showed a standard deviation of $5.60 for the past 60 days. Use the coefficient of variation to determine the variability for each stock. (Round your answers to 2 decimal places, e.g. 2.63.) Coefficient of variation for stock X = 9.5833 % Coefficient of variation for stock Y = 6.4286 % Stock X V has a greater relative variability.Shown here are the top 12 biggest oil and gas companies in the world according to Forbes. Use these as population data and answer the questions that follow. Production Volume Company (million barrels per day) Saudi Aramco (Saudi 12.5 Arabia) Gazprom (Russia) 9.7 NIOC (Iran) 6.4 ExxonMobil Corp. (USA) 5.3 PetroChina (China) 4.4 BP (UK) 4.1 Royal Dutch/Shell 3.9 (NL/UK) Pemex (Mexico) 3.6 Chevron Corp. (USA) 3.5 KPC (Kuwait) 3.2 ADNOC (UAE) 2.9 Sonatrach (Algeria) 2.7a. What are the values of the mean and the median? (Round your answers to 3 decimal places.) Mean = 5.183 Median = 4 b. What are the values of the range and interquartile range? (Round your answers to 1 decimal place.) Range = 9.8 Interquartile range = 2.5 c. What are the values of the variance and standard deviation for these data? (Round your answers to 3 decimal places.) Variance = 2.93 Standard deviation = 2.879 d. What is the z score for ADNOC (UAE)? What is the z score for ExxonMobil Corp. (USA)? (Round your answers to 2 decimal places.) z score for ADNOC (UAE) = -0.854 z score for ExxonMobil Corp. (USA) = 0.422Some numbers are not normally distributed. If the mean of the numbers is 38 and the standard deviation is 6, what proportion of values would fall between 26 and 50? What proportion of values would fall between 14 and 62? Between what two values would 89% of the values fall? ( Round your answers to 2 decimal places.) At least % of the values will fall between 26 and 50. At least % of the values fall between 14 and 62. Between 044 and 0.32 at least 89% of the values fall. A data set contains the fol lowing seven values. 6249135 ( Round the intermediate values to 4 decimal places.) a. Find the range. b. Find the mean absolute deviation. (Round your answer to 4decimal places.) c. Find the population variance. (Round your answer to 4 decimal places.) cl. Find the population standard deviation. (Round your answer to 4decimal places.) e. Find the interquartile range. f. Find the z score for each value. (Round your answers to 2 decimal places) 2 score for 6 = 0.6883 2 score for 2 = 0.9177 2 score for 4 = z score for 9 = z score for 1 = z score for 3 = z score for 5 =