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- th A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, µ, of babies born during the 24"" week of the gestation period. She plans to select a random sample of birth weights of such babies and use the mean of the sample to estimate u. Assuming that the population of th birth weights of babies born during the 24"" week has a standard deviation of 2.6 pounds, what is the minimum sample size needed for the scientist to be 95% confident that her estimate is within 0.5 pounds of µ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) Continue Submit AsQuestion 7 of 7 -/ 1 View Policies Current Attempt in Progress Assume that the annual earnings of all employees with CPA certification and 6 years of experience and working for large firms have a bell-shaped distribution with a mean of $138,000 and a standard deviation of $11,000. Using the empirical rule, find the interval that contains the annual earnings of 68 % of all such employees. ($ i $ i JAA. IIREM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that σ1 = 0.5 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.20 hours per night. Previous studies show that σ2 = 0.7 hour. (a) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ1 − μ2. Round your answer to two decimal places.)(b) Find (or estimate) the P-value. (Round your answer to four decimal places.) (c) Find a 98% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit
- A normal distribution has a mean of u = 50 and 0 = 12 if one score is randomly selected for distribution what is the probability of randomly selectingt a score that is X < 56A standardized exam’s score are normally distributed. In a recent year, the mean test score was 1477 and the standard was 315. The test scores of four students selected at random 1860 1230, 2160, and 1360. Find the Z- score that correspond to each value and determine wether any of the values are unusual. The Z-score for 1860 is-The Z-score for 1230 is-The Z-score for 2160 is-The Z-score for 1360is-REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that σ1 = 0.6 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that σ2 = 0.8 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
- What happens to the t-distribution as the sample size increases?The amounts of sugar in a serving of children's breakfast cereals is normally distributed with a mean of 8.4 grams and a standard deviation of 2.1 grams. For a sample of 15 children's breakfast cereals, what is the probability that the sample mean amount of sugar in a serving for the 15 cereals will be at least than 10 grams? Show how you calculated your result here (type in what you typed on your calculator or computer, the function used on the calculator/computer with value input, etc) Calculation: ___________ Now type in your final simplified or rounded answer, if necessary round your answer to four decimal places. P(x¯<10 grams) = ___________Blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.5. Using chebyshev’s theorem what is the known percentage of women with platelet counts that are within 2 standard deviations of the mean?
- Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the following (a) What percentage of people has an IQ score between 40 and 160? (b) What percentage of people has an IQ score less than 60 or greater than 140? (c) What percentage of people has an IQ score greater than 120? (a) % (Type an integer or a decimal.)Premature-birth Risk Found Higher for Teens (reported in the Sacramento Bee, April 27, 1995, p. A7) The youngest girls [in the study], those aged 13 to 17, were 90 percent more likely than the women in their early 20's to deliver prematurely. "The relative risk was 1.9. But what is the absolute risk for women in their 20's which is used as the baseline?An excess of high values for the cases distributed on a graph results in a positive skew in the data?