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- 4. The lifetime, in years, of a type of small electric motor operating under adverse conditions is T ~Γ(6, 3.6). Whenever the motor fails, it is replaced with another of the same type. Find theprobability that fewer than 6 motors fail within one year.EVALUATE THE FOLLOWING DIFFERENTIAL EQUATIO0N USING BERNOULLI'SIs there a way to solve this w/o using L'Hospital's rule?
- You are using t-test with 15 degrees of freedom to test H0: u=112 vs Ha: u<112, and the rejection was defined to be all the values less than -1.753. What is the implied value of alpha that this test is being performed at?An efficiency study of the morning shift at a factory (7:00 A.M. to 12:00 noon) indicates that an average worker who arrives on the job at 7:00 A.M. will have produced Qunits t hours later, whereQ(t) = -t3 + 9t2 + 15tWhen during the morning shift does the worker’s production reach the point of diminishing returns?Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4 t1/2 cm3. After 100 seconds the radius of the balloon is r = 2.121568836 units? sec cm cm^2 cm^3 cm/sec cm^2/sec cm^3/sec . How fast is the radius changing after 100 seconds? dr dt = units? sec cm cm^2 cm^3 cm/sec cm^2/sec cm^3/sec
- Answers: 1. Fobt = 7.54, reject H0;, do Wilcoxon; Tobt = 90.5, reject H0 2. Fobt = 10.08, reject H0, do Wilcoxon; Zobt = 1.197, do not reject H0 3. t = .163, Do not reject H0; no evidence that the device increases cars' mpgA manufacturing company employs two inspecting devices to sample afraction of their output for quality control purposes. The first inspection monitor isable to accurately detect 99.5% of the defective items it receives, whereas the secondis able to do so in 99.7% of the cases. Assume that four defective items are producedand sent out for inspection. Let X and Y denote the number of items that will beidentified as defective by inspecting devices 1 and 2, respectively. Assume the devicesare independent. Determine(a) the range of the joint probability distribution of X and Y .(b) fXY (x, y).(c) fX(x).(d) E(X).e) fY |X=3(y).If T is nilpotent of index k. Show that Tn , n>1 is nilpotent of index k.
- An SRS of 100 flights by Speedy Airlines showed that 64 were on time. An SRS of 100 flights by Happy Airlines showed that 80 were on time. Let pS be the proportion of on-time flights for all Speedy Airline flights, and let pH be the proportion of all on-time flights for all Happy Airlines flights. Is there evidence of a difference in the on-time rate for the two airlines? To determine this, you test the hypotheses H0 : pS – pH 0, Ha : pS – pH 0. The P-value of your test is 0.0117. Which of the following is an appropriate interpretation of the P-value? a. If the on-time rates for the two airlines are equal, there is a 0.0117 probability of getting samples with a difference as far or farther from zero as these samples. b. If the on-time rates for the two airlines are not equal, the probability of getting samples with a difference as far or farther from zero as these samples is 0.9883. c. The probability of making a Type I error is 0.0117. d. The probability of making a Type II error…If after performing a t-test for comparison of means (alpha= .05) we obtain p=0.0256, what is our conclusion? a. Fail to reject H0 b. Reject H0 c. Reject H1 d. Unable to determine from the information providedUse Simpson's 3/8 rule to compute the approximated solution where f (x) = 1/Cosx + 4 defined at the interval (1,4.5) and n = 7