P(E₁) = P(E2) = P(E3)== 3. Also P(A/E)= 1, P(A/E2) 75 3 60 === 4 P(E3)= 100 100 miin 35 By Bayes' Theorem, P(E₁/A) = P(E₁) P(A/E₁) P(E,) P(A/E)+P(E,) P(A/E)+P(E2) P(A/E₂)
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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.If P(A or B) = 0.801, P(B') = 0.33 and P(A and B) = 0.20. Find i) P(B) ii) P(A)P(A)= 0.23, P(B)= 0.46, P(A and B)= 0.15 Calculate P(A' and B)
- P(A)=P(B)= 0.33, P(A or B) = 0.43 Find P(A and B')Estimate 1/112 using the linearization L(x) of f(x) = x−1 at a = 100. part a) L(112) = part b) Find the actual value of 1/112. (Round your answer to five decimal places.) part c) Calculate the percentage error of Linear Approximation. (Round your answer to three decimal places.)The equation of the normal line to the curve y = -Va that is parallel to -6x +y = 1 (A) y + 3 = -6(x-9) (B) y + 3 = 6(x - 9) %3D (C) y + 3 = 6(x + 9) (D) y – 3 = -6(x+ 9) (E) y - 3 = -6(x - 9)
- If degree of freedom(df) = 20, find the t value(s) for α = 1.0% in two tails(lower and upper tail) ✡✎ +/-2.845 +/-2.145 +2.861 -2.861 If degree of freedom(df) = 2, find the t value for α = 5.0% in one tail( lower tail) ✡✎ -2.920 +2.920 -1.753 2.977 none of the above If degree of freedom(df) = 20, find the t value for α = 1.0% in one tail( lower tail) – 2.528 ✢✎ ☞ ✒✎✕✒✘ -2.539 + 2.539 If n = 20, find the t value for α = 0.5% in one tail (upper tail) 2.861 2.602 ✣✎ 2.977 2.947 none of the above Use the standard normal probability distribution table (Z) to find the following probabilities: P( Z < 1.2) 5871 5478 6543 8849 P( Z > 1.72) 0427 9573 9656 0344 P( Z < -0.42) 0778 9222 3372 6638 P( Z > - 0.42) 0778 9222 3322 6628 P( 2.28 < Z <3.28) 0778 9995 0108 9887 P( -1.20 < Z < 1 .04) 8508 7357 7457 9876 P( -1.52 < Z < -0.09) 0987 0643 0,3998 4641A cup of coffee, cooling off in a room at temperature 23°C, has cooling constant k = 0.083 min ¹. (a) How fast is the coffee cooling (in degrees per minute) when its temperature is T = 71°C? Cooling at the rate = min (b) Use the Linear Approximation to estimate the change in temperature over the next 9s when T = 71°C. Estimated to cool = = °C over the next 9 s (c) The coffee is served at a temperature of 86°C. How long should wait before drinking it if the optimal temperature is 65°C? Waiting time = min you8. After p practice sessions, a student could perform a task in T (p) = 36(p + 1) 3 minutes. Find T'(7) and interpret your answer.