5. A group of doctors are conducting a clinical trial for an experimental cancer drug. The graph below shows theprobability of patient survival as a function of time, t (in months). The functions for Streated (survival probabilityof patients treated by the drug) and Splacebo (survival probability of patients given a placebo) are determined tobe: Streated(t) = e-(15)" and Splacebo (t) = e15t144.(a)"Ise the given function15tPpiacevo \"e-144to calculate%3DSpreatedthe average survival probability ofthe placebo group for the first 10months of the study. Round to 2decimal places.5-0:8-0:6Splacebo-0:40:21020(b)The efficacy of the drug at any timer > 0 can be defined as E(T) = | (Streated(t) – Splacebo (t)) dt.Note: This can be thought of as representing a difference of areas.Use a Riemann sum with 5 sub-intervals of equal width to approximate E(10). Use right endpoints. Roundyour final answer to 2 decimal places.(c)the first T months). Is the drug beneficial atA drug is beneficial if E(T) > 0 (meaning treated subjects have a larger average survival time overmonths? (Aone-sentence answer is enough.)(d)Is the drug beneficial at T = 20? Explain in 1 or 2 sentences.Survival probability

Given that Streatedt=e−t122Splacebot=e−15t144

Answered: A group of doctors are conducting a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Data collected by a psychology professor over a four-year period examined the relationship between class attendance and average test grades in introductory psychology. Results revealed that the correlation between the number of classes attended was positively correlated with the students' average test gradeover the course of the semester (r = 0.35). (a) What is the proportionate reduction in error, or r2, for predicting average test grade from the number of classes attended? (b) Explain what this r2 means for this set of data.
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 4641
A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=140+5 mg/dl and σ=5+1 mg/dl. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured: Once? n=5+2 times n=5+4 times Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.00 6.00 6.50 7.50 8.00 y 25 55 64 66 75 Find a for the equation of the least-squares line y=a+bx given that x=6.6 and y=57. Group of answer choices –57.039 –41.421 57.039 –56.621 –56.679
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:x5.756.257.258.259.25y2218786795What percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line?
Reliability testing of the new 2.0 liter Chevy automotive engine has resulted in a time to failure distribution which is lognormal with = 90,000 mi. and s = 0.60. Find: med %3D a. R(40,000 mi.) b. MTTF and Std. Dev. c. R(90,000|40,000) d. t .90
Suppose the relationship between Y and X is given by: Y = 50 + 3X + error By how much does the expected value of Y change if X decreases by 2 units?
What percentage of pregnancies last beyond 254 days? P(x > 254 days) = P(z >
The heat index (HI) is an estimate of the temperature felt by the human body based on the actual measured air temperature T (in °F) and relative humidity h,. It is given by HI = - 42.379 + 2.049015237 + 10.14333127h, – 0.22475541Th, – (6.83783 × 10-³)T² - (5.481717 x 10-3)h,² + (1.22874 × 10-³)7°h, + (8.5282 - 10-4)Th,² - (1.99 x 10-")T®h,?. a. If the air temperature in your area is 107°F with a relative humidity of 8%, how hot does your body feel? b. If the air temperature and relative humidity is known to be increasing at a rate of 2°F per sec and 1% per sec, resp., how fast is the heat index changing at the moment when the air temperature in your area is 107°F with a relative humidity of 8%?
You were asked to help with analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers AGE at birth (continuous variable in years) and mothers smoking status (the maternal smoking status MSS contains 4 categories “Non-smoker”, “Past-smoker”, “Passive-smoker”, “Smoker”) and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “State Island”). Write down the population model that assumes the effect of mother’s AGE at birth on infant weight BW is DIFFERENT for different levels of maternal smoking status (MSS) when adjusted for BOROUGH variable. Specify the name of each predictor in the model and/or what it means. Make sure that it is clear what each predictor means.
The time to repair a power generator is best described by its pdf m(t) = 333 1sts10 hours %3D 9. (a) Find the probability that a repair will be completed in 6 hours. (b) What is the MTTR? (c) Find the repair rate.
A population of N=15 has a mean =8 one score in the population is changed from X=20 to X-5.What is the value for thr new population mean?

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