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Suppose a random variable X has the following
The random variable X has a Beta distribution with α = 3 and β = 2.
What is the P( 0.33 < X < 0.75 ).
Express your answer as a proportion rounded to 4 decimal places.
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- A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) (i) Round your answer to two decimal places. x = (rounded to two decimal places)(ii) Round your answer to two decimal places. sx = (rounded to two decimal places)(iii) Enter an exact number as an integer, fraction, or decimal. n = (iv) Enter an exact number as an integer, fraction, or decimal. n − 1 = Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a)Consider a random sample from the distribution of Binomial, Poisson, Exponential,Gamma, and normal. Let T4 =∑X /(n + 1). Find the MSE of each statistic and choose the best statistic.
- A population of values has a normal distribution with μ=158.8μ=158.8 and σ=91.9σ=91.9. You intend to draw a random sample of size n=141n=141.Inverse Normal CalculatorFind P10, which is the score separating the bottom 10% scores from the top 90% scores.P10 (for single values) = Find P10, which is the mean separating the bottom 10% means from the top 90% means.P10 (for sample means) = Enter your answers as numbers accurate to 1 decimal place.14. Identifying individuals with a high risk of Alzheimer's disease usually involves a long series of cognitive tests. However, researchers have developed a 7-Minute Screen, which is a quick and easy way to accomplish the same goal. The question is whether the 7-Minute Screen is as effective as the complete series of tests. To address this question, Ijuin et al. (2008) administered both tests to a group of patients and compared the results. The following data represent results similar to those obtained in the study. 18. 7-Minute Screen Cognitive Series Patient 3 11 8. 19 10 22 8. 20 4. 14 13 4 9. 20 14 25 a. Compute the Pearson correlation to measure the degree of relationship between the two test scores. b. Is the correlation statistically significant? Use a two-tailed test with a = .01. c. What percentage of variance for the cognitive scores is predicted from the 7-Minute Screen scores? (Compute the value of r.) 15. For a two-tailed test with a = .05, use Table R 6 to ABCD EFGHCarboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood.t Let x be a random variable representing percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n = 12 blood tests given to a heavy smoker gave the following results (percent carboxyhemoglobin in the blood). Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. 9.1 9.8 10.4 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 (a) Use your calculator to calculate x and s. (Round your answers to four decimal places.) X = S = (b) A long-term population mean u = 10% is considered a health risk. However, a long-term population mean above 10% is considered a…
- Assume the random variable X is normally distributed, with mean μ=47 and standard deviation σ=8. Find the 14th percentile.a normal distribution has a mean of u=60 with o=15. if one score is randomly selected from the distribution, what is the probability that the score will be greater than x=35In the distribution with u = 35 and o = 6, a score of X = 50 correspond to z =
- In a distribution with u = 80 and o = 20, a z-score of z = -1.00 corresponds to an X value of X = 70. O True O FalseThe random variables X is the best described by a normal distribution with = 30 and a = 6. Find the z-score that corresponds to the following X values.:1. X = 212 X = 26.5Let ex be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has a approximately normal distribution with a population mean of 14.0 and population standard deviation equal 2.3. Suppose a female patient had 10 blood test over the past year , and the sample mean HC was determined to be 15.3. With a level of significance a= 0.05, determine whether the patient's HC is higher than the population averages. Specifically do the following: write the data state null hypothesis H0 and the alternate hypothesis H1