Given the normally distributed variable X with mean 18 and standard deviation 2.5, find (a) P(X <10); (b) the value of k such that P(X k) = 0.1814; (d) P(15
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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Suppose a sample Y1, ..., Yn is selected from an exponential distribution with E (Yi) = θ and V (Yi) = θ2. Let θˆ be an estimator of the mean, θ.1. Explain what a parameter is. What is the parameter of interest in this case?2. Name the properties of a good estimator and explain, shortly, what is meant by each. (a)(b) (c)3. Given the properties you discussed in (2) and the parameter of interest identified in (1), what estimator would you propose?4. What would the sampling distribution of this estimator be? Why?For data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula is where P=1- 1/k2 p is the minimum percentage of scores that fall within kk standard deviations on both sides of the mean. Use this formula to answer the following questions. b) If you have scores that are normally distributed, find the percentage of scores that fall within 3.3 standard deviations on both sides of the mean? c) If you have scores and you don't know if they are normally distributed, how many standard deviations on both sides of the mean do we need to go to have 35 percent of the scores? Note: To answer part c you will need to solve the equation for k.k. A manufacturer knows that their items have a normally distributed length, with a mean of 5.3 inches, and standard deviation of 1.5 inches.If one item is chosen at random, what is the probability that it is less than 8.3 inches long?
- If E(X) = 3 and Var(X) = 2, which of the following is equal to E(2X + 4x²) A. 20 B. 30 C. 40 D. 50 If the intelligence quotients (IQ) of all human beings are assumed to be normally distributed with mean equal to 100, and standard deviation equal to 10, then which of the following is TRUE? A. The distribution of the IQ of all human beings is positively skewed. B. At least 50% of all human beings have IQ less than or equal to 100. C. The probability of selecting a human being with an IQ equal to 100 is 0.5. D. The probability that the IQ of a randomly selected human being is inside the interval (90, 110) is approximately equal to 0.95.(d) Give E(X). Answer= (e) Give E(Y). Answer= (f) Give E(X| Y = 3). Answer= (g) Give the standard deviation of Y. Answer=Use the formula to find the standard error of the distribution of differences in sample means, I – X2. Samples of size 26 from Population 1 with mean 5.6 and standard deviation 3.9 and samples of size 45 from Population 2 with mean 8.1 and standard deviation 7.6 Round your answer for the standard error to two decimal places. standard error =
- For a football game in the National Football League, let y = difference between the number of points scored by the home team and the away team (so y > 0 if the home team wins). Let x bet the predicted difference according to the Las Vegas betting spread. For the 768 NFL games played between 2003 and 2006, output follows. Predictor Coefficient SE Coef T P Constant -0.4022 0.5233 -0.77 0.442 BP 1.0251 0.0824 12.44 0.000 (a) We wish to test the null hypothesis that the Las Vegas predictions are unbiased. This will correspond with ? = 0 and ? = b) Based on the results shown in the table, is there much evidence that the sample fit differs from the model ?y = ? + ?x, with values of alpha and beta above? Why?The variable X, is the carbon monoxide concentration in air, and ten measurements are obtained as follows: 10.25, 10.37, 10.66, 10.47, 10.56, 10.22, 10.44, 10.38, 10.63, 10.40 mg/m3 . (i) Test whether the mean concentration of carbon monoxide in air is 10.00 mg/m3 . (ii) Calculate the power of the above test if the mean concentration of carbon monoxide in the alternative hypothesis is assumed to be 10.75mg/m3 .A researcher believes at 49% of people who grew up as the only child have an IQ score over 100. However, unknown to the researcher this figure is actually 50% which is the same as the general population. To attempt to find evidence for the claim, the researcher is going to take a random sample of 400 people who grew up as an only child. Let X be the proportion of people in the sample with an IQ score above 100. (a) find the mean of C (b) find the standard deviation of X (c) compute the approximation for P(x >0.49) , which is the probability that there will be 49% or more with the IQ scores over 100 in the sample. Round your answer to four decimal places. * greater than sign, is supposed to be greater than or equal to sign*
- Suppose it is desired to estimate the variance of the tensile strength of a particular type of thread. For 21 pieces of this type of thread, E(X; - Xave)² = 2000. What is the point estimte of the true standard deviation of the tensile strength of this thread?(Q2) A store room measured in length equal to (5m + 3 cm), measured width equal to (4m 2cm) measured height equal to (3m + 4 cm), find the total volume of this room and the standard deviation.b. Math Score(x) 4 7 10 13 16 Frequency(f) 4SEE MORE QUESTIONS
