5.3.6. What "confidence" would be associated with each of the following intervals? Assume that the random vari- able Y is normally distributed and that σ is known. (a) (-1.64 +2.33.) (b) (-∞, +2.58.) y (c) ( − 1.64)
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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.Let XX represent the full height of certain species of tree. Assume that XX is normally distributed with a mean of 217 feet and a standard deviation of 34 feet.Find the probability that the full height of a randomly selected tree is less than 248 feet. P(X<248)P(X<248) = Enter your answer as a number accurate to 3 decimal places.A sample of 2000 observations has a mean of 74 and a standard deviation of 12. Using Chebyshev’s theorem, find the minimum percentage of the observations that fall in the intervals x +/- 2s, x +/- 2.5s and x +/- 3s Note that x +/- 2s represents the interval x - 2s to x + 2s, and so on Also note that s is symbol for standard deviation in this example
- ) = P ( Z < ) The mean number of hours of sleep that a college student gets per night is 6 hours with a standard deviation of 3 hours. A random sample of forty students is observed. It is of interest to determine the probability that a single student gets less than 5 hours of sleep at night. Identify the correct formula for solving. P (X < 5) = P ( 2 (6–5) Z < 3 ®,") O P(X <5) = P ( Z < (5–6) 3 (5–6) P (X < 5) = P ( Z < 3 V40 P(X < 5) = P ( Z < ®,") O P(X < 5) = P(z < ") (5-6) 9 (6–5) 3 V40 P (X < 5) = P ( Z < (5–6) 9. V40 (5–6) P (X < 5) = P (Z V40 O None of the above / Unable to solveChebyshev's Theorem states that for any set of numbers, the fraction that will like within k Standard deviations of the mean is at least 1- 1/k2. Use this theorem to find the fraxtion of all the numbers of a data that must lie within 3 standard deviations from the mean.Q.5. The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 8 minutes. (a) Find the probability that the time interval between two successive barges is less than 5 minutes. (b) Find a time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t.
- 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)2.5.5.) The cumulative distribution function F(x) of a random variable X is given by 0, -8{85, 60, 95, 95, 100, 75, 52, 60, 99, 80}b. ((∑(xi – X)2)/(N – 1))1/2solve the standard deviation.Suppose that f (x) = (3/2)x2 for −1< x < 1. Determine the mean and standard deviation of X.o 5. In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between - 10, 25 8.5 and 12 hours. Give a mathematical expression for the probability density function of battery life. b. What is the probability that the battery life for an iPad Mini will be 10 hours or less? a. с. What is the probability that the battery life for an iPad Mini will be at least 11 hours? d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours? In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours? X e. Callu ndina bu(26) Let X b(8,- Var-x) and distribution function.SEE MORE QUESTIONS