Hello expert, I need to solve the question step by step and in clear writing If he X~N(μ, σ²) 1) The mean deviation in this distribution is 2) Q1 0.670, Q3 ==μ + 0.67σ σ
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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.Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.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.
- The deviation of each observation (x) from the mean of the predictor variable is positive for every point in what quadrants? * Y (2) 1) 3 4)Please do not give solution in image format thanku The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 70, and the standard deviation is 2. You wish to test H0 : μ =70 versus H1 : μ ≠70 with a sample n = 5 specimens. Find β for the case where the true mean heat evolved is 73. Use the α that you calculated in question 6. Report to three digits after decimal point Problem #6: α= 0.907I need help with these two questions. Here are the data table if needed. The absolute viscosity for sunflower oil is supposed to average 0.0311 Pa⋅s at 38 ∘C. Suppose a food scientist collects a random sample of 4 quantities of sunflower oil and computes the mean viscosity for his sample to be x¯=0.0318 Pa⋅s at 38 ∘C. Assume that measurement errors are normally distributed and that the population standard deviation of sunflower oil viscosity is known to be σ=0.0009 Pa⋅s. The scientist will use a one‑sample z‑test for a mean, at a significance level of α=0.01, to evaluate the null hypothesis, H0:μ=0.0311 Pa⋅s against the alternative hypothesis, H1:μ≠0.0311 Pa⋅s. Complete the scientist's analysis by calculating the value of the one-sample z‑statistic, the p‑value, and then deciding whether to reject the null hypothesis. First, compute the z‑statistic, z. Provide your answer precise to two decimal places. Avoid rounding within calculations. z= Determine the…
- #19 solve using applications of normal distributionApproximate the population mean and standard deviation of age for males. By the way, to find the midpoints we are adding vertically and then dividing by 2 (ex: 0+10/2=5, 10+20/2=15).A population of values has a normal distribution with mean of 159.4 and standard deviation of 80.5. You sample 217 values from the population. a) Get the z-score for a sample mean of 144.1. For this problem you use the z score formula z=(¯x−μ)√nσz=(x¯-μ)nσ b) This z-score tells you how many the sample mean of 144.1 is above or below the population mean μμ . c) Find the probability that a sample mean is greater than 144.1. Enter your numerical answers as numbers accurate to at least 4 decimal places.
- a b Absolute standard deviation = Coefficient of variation = y = 1.20 (+0.02) x 10-8-3.60(±0.2) × 10-⁹ x Result = Absolute standard deviation = Coefficient of variation = C Result = d y=90.95 (±0.08) - 89.40(±0.06) +0.200(+0.004) Absolute standard deviation == Coefficient of variation = Result = ± y= y = 0.0040 (+0.0005) x 10.28 (+0.02) × 395(+1) Result = ± Absolute standard deviation = Coefficient of variation = % 329(+0.03) x 10-14 1.47 (+0.04) x 10-16 % % H % ±You have information to suggest that a certain continuous variable of a population has a mean of μ = 9.13 and a standard deviation of o = 6.67. You are to randomly pick n = 71 individuals from this population and observe the value of the population variable on each. This value is to measured as X₁. After the random sample of n = 71 has been taken, you are asked to consider the behavior of the statistic X. (a) Complete the statement below. Use as many decimals as you can. The distribution of X is approximately Normal with a mean x = 9.13 and a standard deviation x = 0.7916 (b) Find the probability that mean of the sample of n = 71 is between 8.53 and 9.53. Use at least four decimals in your z-values, and enter your answer to at least four decimals.The regression line for Y vs X is given by Y = 0.82X + 59.1. The standard deviations for X and Y are 1.5 and 2.2 respectively. Suppose now we construct a regression line that uses Y to predict X. The predicted average increase of X when Y is increased by 1 unit is ______________. (Give your answer correct to 2 decimal places.)