Poblems 287 Tat: Make use of the formula for the moment generating function of a normal random variable. A The following are, in minutes, travel times to work over a sequence of 10 days. 42, 28, 53, 57, 67, 39, 35, 50, 44, 39 Assuming an underlying lognormal distribution, use the data to estimate the mean travel time. 8. An electric scale gives a reading equal to the true weight plus a random error that is normally distributed with mean 0 and standard deviation o = .1 mg. Suppose that the results of five successive weighings of the same object are as follows: 3.142, 3.163, 3.155, 3.150, 3.141. (a) Determine a 95 percent confidence interval estimate of the true weight. (b) Determine a 99 percent confidence interval estimate of the true weight. 9. The PCB concentration of a fish caught in Lake Michigan was measured by a technique that is known to result in an error of measurement that is normally distributed with a standard deviation of .08 ppm (parts per million). Suppose the results of 10 independent measurements of this fish are 11.2, 12.4, 10.8, 11.6, 12.5, 10.1, 11.0, 12.2, 12.4, 10.6 (a) Give a 95 percent confidence interval for the PCB level of this fish. (b) Give a 95 percent lower confidence interval. (c) Give a 95 percent upper confidence interval. 10. The standard deviation of test scores on a certain achievement test is 11.3. If a random sample of 81 students had a sample mean score of 74.6, find a 90 percent confidence interval estimate for the average score of all students. 11. Let X1,...,X, X+1 be a sample from a normal population having an unknown mean u and variance 1. Let Xn = E X;/n be the average of the first n of them. %3D %3D1 (a) What is the distribution of Xn+1- Xn? (b) If X = 4, give an interval that, with 90 percent confidence, will contain the value of X+1. 12. If X1,..., X, is a sample from a normal population whose mean u is unknown but whose variance o? is known, show that (-0, X+ Z0//n) is a 100(1- a) percent lower confidence interval for u. . A sample of 20 cigarettes is tested to determine nicotine content and the average value observed was 1.2 mg. Compute a 99 percent two-sided confidence inter- vai for the mean nicotine content of a cigarette if it is known that the standard deviation of a cigarette's nicotine content is o .2 mg. %3D

Q: Question 12

A: Given: Value of the trading card = $155 (in 2009) Each year increases by = 4.8% = 0.048 To…

Q: Do dominant and subordinate individuals differ in the means of giggle spectral CV?

A: For Group : Dominant Individual Standard Deviation, s: 0.05410 Count, N: 9 Sum, Σx: 2.755…

Q: Question 26

A: We have given a graph which represent the derivative f' of some function f. we have to draw the…

Q: 60. f -1 | f' f" -1

A: According to the sign chart, we have

Q: question 32

A: (32)   (a)   State the hypotheses. That is, the average activating temperature is at least 135 F.…

Q: Question 7

A: 7) (a) The given parametric equations are  x=t+2 and y=t2-1 and t∈-3, 3. Sketch the graph of the…

Q: Question 5

A: From the provided information, Number of trials (n) = 100 Probability of getting tails (p) = 0.5

Q: Question 12

A: (12)(a) Given, f(x)=2x-6 such that f:ℝ→ℝThe function f(x) is a linear function. The f(x) is defined…

Q: Question 12

A: We are given the following shapes. For (a), We need to find the volume of the box as a function of…

Q: Question 20

A: Given Data :  General form of the sequence an=2(an-1)+1, a1=4 To Find : The first four terms of the…

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.