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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.The expectation of X, which is also known as the mean or average, is E(X) = 7 and the Variance of X is var(X) =4. Using the equation Y = 11X + 81. What are the expected value E(Y), variance VAR(Y), and standard deviation SD(Y) of this expression.Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 = 3.
- 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.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*When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 5 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)equals=0.00762,where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W) denote, and what is its value? What does P(W) represent? P(W)=
- The variation of Y around its mean can be decomposed into which two parts?The probabilities of various numbers of failures in a mechanical test are as follows: Pr[0 failures] = 0.21, Pr[l failure] = 0.43, Pr[2 failures] = 0.28, Pr[3 failures] = 0.08, Pr[more than 3 failures] = 0. (a)Show this probability function as a graph with number of failures in x-axis and probability in y-axis. (b)Sketch a graph of the corresponding cumulative distribution function. Hint: cumulative probability in y-axis (c)What is the expected number of failures, E, or the mathematical expectation of the number of failures?Suppose that f (x) = x / 8 for 3 < x < 5. Determine the mean and variance of x.
- Let f(r) 3" and g(r) 1. . and evaluate the following: 3. g(- 3 g(- 1)= 5. f(- 2): 6. f( – 3) = 3%3= 7. f(2) + g( – 2) = 8. f(2)-g(-2) = SubmitThe mean hourly wage W (in dollars) of chemists in the United States from 2000 through 2014 can be modelled by W=0.903t+26.08, 0≤t≤14 where t represents the year, t = 0 corresponding to 2000. (a) Based from the model, when was the mean hourly wage at least $30, but not more than $32?(x₁,...,xn) be a data set, and denote its sample standard deviation with s. Let yį = ax; + b. (a) Show that sy = |a|sx, where sy is the sample standard deviation of y = (y₁,..., Yn). (b) Show that Median(y) = a. Median(x) + b. Let x = (c) If a > 0, can you write the relation between Q1(y) and Q1(x)? What happens if a < 0? Note: Q1(x) (or Q1(y)) denotes the first quartile of the distribution of the random variable x (or y)