Question

(6 points) You purchase a chainsaw, and can buy one of two types of batteries to power it, namely Duxcell and Infinitycell. Batteries of each type have lifetimes before recharge that can be assumed independent and Normally distributed. The mean and standard deviation of the lifetimes of the Duxcell batteries are 10 and 2 minutes respectively, the mean and standard deviation for the Infinitycell batteries are 16 and 3 minutes respectively. Parta) What is the probability that a Duxcell battery will last longer than an Infinitycell battery? Give your answer to four decimal places. 0.5481 Part b) What is the probability that an Infinitycell battery will last more than twice as long as a Duxcell battery? Give your answer to four decimal places. 0.7119 Part c) You are going to cut down a large tree and do not want to break off from the job to recharge your chainsaw battery. You buy two Duxcell batteries, and plan to use one until it runs out of power, after which you immediately replace it with the second battery. How long (in minutes) can the job last so that with probability 0.75 you can complete the job using the two Duxcell batteries in sequence? Provide your answer to 1 decimal place. 15.0

Answer 1

Let the lifetime of Duxcell batteries are XaN(10, 22) and the lifetime of Infinity cell. batteries will be Y N N (16,32). a. The distribution of X-Y~N(10-16, 22, 3) - (-6,13) The Required probability P(x>y) - PCX-Y>0). P(X>Y - P (z > Ot6 17 sundor P(x>Y) = P(Z > 1.6641005 P (874) =(-1.6641005) PCX >Y) - 65421 (0.0537 0 00 N13 HOTES CS Scanned with CamScanner

00 10 b). The distribution of cx de ax- YN (20-16, 4(22) + 24 ) = N(4,25) N(4, 52). 10 The required probability P(Y>ax - P (2x-yeo) P(Y>2x2 = P (2 <0 ) P(432x) - P(-0.8) PCY>ax) = 0 (-0.8).= 0.9119 C. The lifetime of two Duxcell batteries when replaced offer the fost one is faulty is x = X, 4X2 ~ N(20,2622)) De Let the job can last Xas minutes with 6.75. probability of completion. Then CS Scanned with -CamScanner