Let R be the actual resistance of a resistor that is selected at random from a batch of 100 N' resistors produced by a certain factory. The '100 N’ resistors produced by the factory are of course not exactly 100 N each. They are actually random with mean uR deviation ơR Now, let's suppose that the resistance of our randomly selected reistor from this batch is measured twice with an ohmmeter. Let M¡ and M2 denote the measured values. Then M1 = R+Ej and M, = R+ E2, where E, and E, are the measurement errors. Suppose further that E¡ and E, are random with means zero and standard deviations 1 N. Assuming that R, E1, and E2 are mutually independent, = 100 N and standard 2 Ω. %3D %3D %3D a) find the standard deviations of M¡ and M2, b) show that the expected value of M, M2 is just equal to the expected value of R2, c) show also that E [M¡]E [M2] = E² [R].

27. In a memory experiment, Alice is able to memorize words at a rate given by m′(t)=−0.009t2+0.5t. In the same memory​ experiment, Ben is able to memorize words at the rate given by M′(t)=−0.003t2+0.5t.   ​a) Who has the higher rate of memorization?     Ben   Alice   ​b) How many more words does that person memorize from t=0 to t=10 ​(during the first 10 minutes of the experiment)?   words ​(Simplify your​ answer.)   ​c) Over the first 10 minutes of the​ experiment, on​ average, how many words per minute did Alice memorize?   words ​(Simplify your​ answer.) ​d) Over the first 10 minutes of the experiment, on​ average, how many words per minute did Ben​ memorize?   words ​(Simplify your​ answer.)

5.5 problem 24

Find C(n, x)p*q" - *for the given values of n, x, and p. (Round your answer to four decimal places.) n = 8, x = 5, p =

A certain model of car can be ordered with either a large or small engine. The mean number of miles per gallon for cars with a small engine is 6.8. An automotive engineer thinks that the mean for cars with the larger engine is higher than this. State the appropriate null and alternate hypotheses. The null hypothesis is Hoμ (Choose one) The alternate hypothesis is H₁ μu (Choose one) ×

For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol μμ , e.g. mu >> 1 for the mean is greater than 1, mu << 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. Please do not include units such as "mm" or "$" in your answer.) (a) The diameter of a spindle in a small motor is supposed to be 5.2 millimeters (mm) with a standard deviation of 0.15 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 13 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 5.34 mm.H0 :    Ha :      (b) Harry thinks that prices in Caldwell are lower than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $17.55 with standard deviation $0.72. He takes a sample from 4 local Caldwell stores and finds the average…