Prove the following using strong induction. Suppose you are gifted a collection of 3n pokéballs; all of the the pokéballs have the same size and weight except for one which is slightly heavier, and otherwise look and feel exactly the same as the others. You are tasked with identifying the heavy pokéball and have at your disposal a set of balancing scales which can be used to compare the weights of two collections of pokéballs. The scales can show whether the two collections have the same weight, or can show which collection is heavier if the weights are different. Prove using strong induction that you can identify the heavy pokéball out of 3n pokéballs using n weighing operations.

A researcher is interested in the relationship between birth order and personality.  A sample of n=90 people is obtained, all of whom grew up in families as one of three children.  Each person is given a personality test, and the researcher also records the person's birth order position (1st born, 2nd, or 3rd).  The frequencies from this study are shown in the following table.  Birth Position   1st 2nd 3rd Outgoing 14 31 20 Reserved 18 19 6 What are the expected frequencies for the conditions below?

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What is the meaning of x ̅ ~ N (50, 2)?   1. The Sampling distribution is distributed normally with a mean of 50 and a standard deviation of 2   2. Sampling distribution of x is distributed normally with a mean of 2 and a standard deviation of 50   3. x is normally distributed with a mean of 50 and a standard deviation of 2   4. x-bar is normally distributed with a mean of 2 and a standard deviation of 50

Below n is the sample size, p is the population and p is the sample proportion.use the central limit theorem and th to-84 probability n=148 P=0.14

(3) The Elon Company manufactures parts for an aircraft company using three computerized numerical controlled (CNC) turning centers. The company has to decide which machines are capable of producing a specific part with design specifications of 0.0970 inch ± 0.015 inch. The machines have the following parameters: Machine 1 (x= 0.0995, o = 0.004); Machine 2 ( = 0.1002, o = 0.009); Machine 3 (x = 0.095, o = 0.005). Determine which machines (if any) can produce the products within the design specifications. ||

A certain reagent is created to test for an infectious disease. The test has anaccuracy rate of p = 90%, and the accuracy does not depend on whether or not thepatient is actually infected. a. If four people are tested for the disease, what is the probability that at leastthree of them receive accurate test results? b. In an area where q = 5% of people are infected, a man’s test result ispositive. What is probability that it is a false positive (which means that he is notinfected but the test is positive due to inaccuracy)?   *please solve for a-b, type or neatly  write your answers on paper, NO EXCEL* thank you !

A shipping company believes that the variation in the cost of customer's shipment can be explained by differences in the weight of the package being To investigate whether this relationship useful, a random sample of 20 customer shipments was selected, and the weight and the cost for each shipment were recorded. the following results were obtained: x y 8 11 6 8 5 11 7 11 12 17 9 11 17 27 13 16 8 9 18 25 17 21 17 24 10 16 20 24 9 21 5 10 13 21 6 16 6 11 12 20   Compute the linear regression model based on the sample data. Interpret the slope and interpret the Estimate the cost if the weight of the shipment is

What is the meaning of x ~ N (50, 20)?   1. Sampling distribution of x is distributed with a mean of 20 and a standard deviation of 50   2. x-bar is normally distributed with a mean of 20 and a standard deviation of 50   3. x is normally distributed with a mean of 50 and a standard deviation of 20   4. Sampling distribution of x is distributed with a mean of  50 and a standard deviation of 20

Lew Pherson and Vera Collier are friends whoare employed by different CPA firms. One day during lunch they are discussing theimportance of internal control in determining the amount of audit evidence requiredfor an engagement. Pherson expresses the view that internal control must be evaluatedcarefully in all companies, regardless of their size or whether they are publicly held,in a similar manner. His CPA firm requires a standard internal control questionnaireon every audit as well as a flowchart of every transaction area. In addition, he says thefirm requires a careful evaluation of the system and a modification in the evidenceaccumulated based on the controls and deficiencies in the system.Collier responds by saying she believes that internal control cannot be adequate inmany of the small companies she audits; therefore, she simply ignores internal controland acts under the assumption of inadequate controls. She goes on to say, “Why should Ispend a lot of time obtaining an…