If X ~ N(u, o?) and the standard normal variable Z is such that Z(0, 1), then p(Z < -0.84) is (A) 0.2005 (B) 0.7995 (E) None of the options (C) 0 (D) 1 Select one: O A.. О В. С. OD. O ..
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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.show that 1-2% show that B(wn) p(ntt, n+t) =표산에.The variation of Y around its mean can be decomposed into which two parts?
- Suppose that Yt is the monthly value of the number of new home construction projects started in the United States. Because of the weather, Yt has a pronounced seasonal pattern; for example, housing starts are low in January and high in June. Let μJan denote the average value of housing starts in January and let μFeb, μMar,. . . . , μDec denote the average values in the other months. Show that the values of μJan, μFeb, . . . , μDec can be estimated from the OLS regression Yt = β0 + β1Febt + β2Mart + . . . .+ β11Dect + ut, where Febt is a binary variable equal to 1 if t February, Mart is a binary variable equal to 1 if t is March, and so forth.Suppose that f(x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.Interpret the value of P(B')
- Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.Suppose that the 101 randomly selected eighth-grade students (mentioned in question 6) took a “practice” test similar to the official standardized test a month before the official test was administered. The researchers reported that the (two-tailed) statistical test of the difference between the practice and official test scores resulted in t100 = -2.32, p < .05. (a) Given that the difference score was computed as D = (practice score – official score), do the reported results indicate that students scored significantly higher or lower on the official test relative to the practice test? Explain. (b) If we constructed the corresponding 95% confidence interval for the mean difference (between the practice and official test scores) in the population, would it include zero? Explain.LET A=0 -> Z=25
- Suppose that a random man's weight from a certain population is M~ Normal (μ = 200, o²49) and a random woman's weight is W ~ Normal( 140, o² = 25). If M and W are independent, what is the variance of the difference between a man's weight and a woman's weight, i.e. Var (M-W)? (a) 340 (b) 24 (c) 140 (d) 200 (e) None of the aboveP(z>2) =?Assume that the entire sample has 2 positive observations and 6 negatives observations. Variable X1: at the left branch has 2 positive observations and 4 negatives observations;at the right branch has 6 positive observations and 6 negatives observations. What is the information gain or reduction in uncertainty of X1 using the Gini index? (round to two decimal spaces)
