Concept explainers
As in Examples 1 and 2, use (a) the binomial distribution; (b) the corresponding normal approximation, to find the probabilities of each of the following:
Verify equations ( 8.6 ). Hints: In
What is
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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.arrow_forward- (Sec. 6.1) Using a long rod that has length µ (unknown), you are going to lay out a square plot in which the length of each side is µ. Thus the area of the plot will be µ². However, because you do not know the value of µ, you decide to make n independent measurements X1,...,X, of the length. Assume that each X; has mean µ and variance o². (a) Show that X² is not an unbiased estimator for the area of the square plot µ². [Hint: for any rv Y, E[Y²] = V[Y] + E[Y]². Apply this for Y = X.] (b) For what value of k is the estimator X² – kS² unbiased for µ²?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill