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Suppose that, in flight, airplane engines will fail (i.e. break down) with probability 1 - p, independently from engine to engine. An airplane needs a majority of its engines operative to complete a successful flight. (Note 1: a majority of engines operative means that more engines are working than not working; Note 2: if 1 - p is the probability of an engine failing, then p is the probability that the engine is working.) a) If p = 4/5, what is the prob ability that a 3 - engine plane will complete a successful flight? b) If p = 2/3, what is the probability that a 5 - engine plane will complete a successful flight? c) What is the standard deviation of the number of working engines for a 5 - engine plane? d) Suppose the factory which manufactures the engines has undergone upgrades to improve their engines. With the upgrades engine failures only occur in 1 out of 400 engines. There are 275 newly manufactured engines waiting to be shipped. Write out the expression (do n ot solve) to find the probability that 1 or 2 of these new engines will fail. e) Is there an appropriate approximation that can be used to det ermine the probability in part d )? Explain why or why not and then use that approximation to find this probability
Based on a sample of 49 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to ma ke various estimates. a) Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)
Consider a random sample of six families who are asked if their children have an influence on their vacation destination.
Find a 90% confidence interval for the mean decibel level µ for this type of transit vehicle.
Let X denote number of students which were on bus carrying this arbitarily selected student. One of the 4 bus drivers is also arbitarily selected. Calculate expectations and variances of X.
Find the mean lifetime of TV tubes. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
These individuals are then examined and categorized as to whether they have a heart disorder. The observed frequencies are as follows:
Normal population having a standard deviation of 0.04, what is the probability that the mean of a random sample of size 25 will be "off" by at most 0.02?
Perform the appropriate test of hypothesis to determine whether Kim's average time has changed. Use alpha=.01. Compute the power of the test if Kim's actual mean swimming time is 147.3 seconds. Interpret the results.
At the .05 level of significance, is there evidence of a difference in variability in the shipping time between the two outlets? What decision should the carpet manufacturer make?
Can the president conclude that the average family income at his school is significantly different than the population mean family income of the reported university?
Find the probability of type I error if exactly 60% of the voters favor the use of these fuels. What is the type II error probability if 75% of the voters favor this action?
If Stephenson wishes to maximize its total market value, would you recommend that it issue debt or equity to finance the land purchase? Explain.
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