X~B (n = 15, p = 0.4) By using the normal approximation to the binomial distribution find the probability P(X = 4). NOTE: (0.5: Continuity correction)
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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.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.Can the average rate of change of a function be constant?
- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Determine the slope of the normal to f(x) = /2r – 18 at x= 3?Determine the equation of the normal line to the graph of the function in the picture at x=1.
- Q2\ For normal distribution find : al z-1.28 Q3\ Find the equation that represent the relation between (x and y): X 1 10 y 2 3 4 5 20 30 40 50Call: lm(formula = Sales ~ Price + Urban + US) Residuals: Min 1Q Median 3Q Max -6.9206 -1.6220 -0.0564 1.5786 7.0581 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 13.043469 0.651012 20.036 < 2e-16 *** Price -0.054459 0.005242 -10.389 < 2e-16 *** UrbanYes -0.021916 0.271650 -0.081 0.936 USYes 1.200573 0.259042 4.635 4.86e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.472 on 396 degrees of freedom Multiple R-squared: 0.2393, Adjusted R-squared: 0.2335 p-value: < 2.2e-16F-statistic: 41.52 on 3 and 396 DF, p-value: < 2.2e-16 Which of the following statement is wrong? Sales = 13.043469 - 0.054459×Price - 0.021916×Urban + 1.200573×USwith Urban = 1 if the store is in an urban location and 0 if not,and US = 1 if the store is in the US and 0 if not. Sales = 13.043469 - 0.054459×Price -…