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- Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with ? = 4 and ? = 2. (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = V(X) = (b) Compute P(X ≤ 0.3). (Round your answer to four decimal places.)(c) Compute P(0.3 ≤ X ≤ 0.7). (Round your answer to four decimal places.)A sample of 56 research cotton samples resulted in asample average percentage elongation of 8.17 and asample standard deviation of 1.42 (“An ApparentRelation Between the Spiral Angle f, the PercentElongation E1, and the Dimensions of the CottonFiber,” Textile Research J., 1978: 407–410). Calculatea 95% large-sample CI for the true average percentageelongation m. What assumptions are you making aboutthe distribution of percentage elongation?Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between −2.09 and −0.96 and draw a sketch of the region. What is the probability?
- Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between −0.81 and −0.01 and draw a sketch of the regionIn a t-distribution, what is the area under the curve that is to the right of t=2.048 and with df=28?Find the area under the standard normal curve to the left of z = 2.11
- Find the area under the t-curve to the right of t = 2.539 (sample size n=20)In a random sample of size 42, 34 people say they generally get less than 8 hours of sleep a night. Calculate the point estimates ˆpp^ and ˆqq^.pˆp^= qˆq^=Report the answer to three decimal places.In a test of H0: p = .43 versus Ha: p ≠ .43, a sample of size 1500 leads to a p-value of 0.087. Which of the following must be true if a = 0.05? A. The Ho should be rejected at the 5% level B. The Ho should fail to be rejected at the 5% level C. The Ho should be accepted at the 5% level