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Chapter 4 Define a discrete random variable:Give an example of a discrete variable.Define a continuous random variable: Give an example of a continuous random variable:A fair coin is tossed three times. Let X be the number of heads observed.Construct a probability distribution of X.Find the probability that two heads are observed.Find the probability that at least 1 tail is observed. Write the mean/expected value formula of a discrete random variable here:Write the variance formula of a discrete random variable here:Write the standard deviation equation of a discrete random variable here:Find the expected value of the discrete random variable X of the following distribution.x-2012P(x)0.210.340.240.21E(x)=0.24With the found mean, find the variance and standard deviation of the above distribution.(Like HW 4, Question 12). Kat and the attendees decide to take a field trip to Wawa. While we’re there, I spot a lottery ticket machine. The chance of winning from a lottery ticket is 1 in 300,000. I decide to spend $2 and hope to win the $950,000 prize. Calculate my net expected for this ticket.Define the Binomial probability experiment (Hint: what are the requirements of a binomial probability experiment).What does n stand for and what does p stand for?What are some examples of binomial random variables?A multiple-choice test has 25 questions, each with five question choices. A student decides to Christmas tree the exam. We want to know the questions they get right. What is our success? Amount of questions right What is our failure? Questions wrong What is our n? 25What is our p? = 0.20What is the probability that he gets exactly 10 right? What is the probability that he gets more than 12 right?What is the probability that he gets at least 8 right?What is the probability that he gets less than 14 right?What is the probability he gets no more than 15 right? the probability formula for a binomial random variable:Write the mean equation of a binomial random variable:Write the equation to find standard deviation of a binomial random variable:For a statistics class, we play a true or false question game that has 30 questions. The probability to get one correct is 50%. Find the probability of getting 17 right. Chapter 5What does the function f(x)= 1/d-c for the uniform distribution?What is the formula to find the probability in the interval a<x<b?How to find the mean for the uniform distribution? How to find the standard deviation of the uniform distribution?Kat loves coffee and decides to buy a Keurig from a neighbor. However, the amount of coffee dispersed into a single cup of coffee follows an equally likely distribution over the interval 4oz to 12oz.Draw the uniform distribution.Determine the mean.Determine the standard deviation.For a single cup of coffee, what is the probability at least 7 oz are dispensed?What are the properties of a normal distribution?Does the normal distribution follow the Empirical Rule?What is the formula used to transform X into a Z-score ?Remember! The table tells you the area in the z-distribution between 0 (mean) and some z-score.What is the probability that Z is between p(0<z<0.29)?What is the probability that z is between p(0<z<2.1)?How about p(-2.1<z<0)?How about P(z>1.1)? (Hint: A+B = 0.5, where A is the area given between 0 and a z score and B is the area we’re finding). How about P(z<1.1)? (Hint: 0.5 + A)Get comfortable with the normal distribution calculator on statcruch!The time it takes for a UCF statistics student to complete a statistics test follows a normal distribution with a mean of 40 minutes and a standard distribution of 6 minutes. We select one student at random.What is the probability that it takes a student less than 24 minutes to complete the exam? P(x<24)The height of UCF students that are male follows a normal distribution with a mean of 70 inches and a standard deviation of 3 inches. What is the proportion of UCF students that are male with a height between 67 inches and 73 inches?What about between 68.25 and 72.75?Would there be a probability at exactly 69.28?Find a value of the standard normal random variable z, call it Zo, such that the following probabilities are satisfied.P(z<zo)= 0.0376Interpret the above in terms of area.What is our clue?How can we use the clue in our Z-score table? (Hint: 0.5-A)How about using technology?The height of UCF students that are male follows a normal distribution with a mean of 70 inches and a standard deviation of 3 inches. If you are taller than 60% of other UCF students that are male, you get a free Foxtail drink. What is the height requirement? (Hint, they gave us probability, so we need to find Z-score) (Since must be taller than 60% and z-score is between 0 and a z-score)Chapter 6Define a parameter:What are examples of a parameter?What are some numerical descriptive measures?What is a sample statistic?Does the sample mean, sample median fall closer or neither to the population mean after a single trial? What is a point estimator?What is the minimum-variance unbiased estimator for the population mean? Does it need a sampling distribution that is unbiased and has a small standard deviation? (Hint: refer to 6.2)Why can’t x be trusted?How do we track the behavior of x?Does the meaning of the sampling distribution of x equal the mean of the sampled population?How do we find the standard deviation of the sampling distribution of x ? (formula)What is the Central Limit Theorem?What can make the sampling distribution of x a normal distribution? (View 6.3 and the rabbit example video in 6.3)How do we find the position of x value relative to the mean? (Hint: Z-score formula found in 6.3)The weight of a baby beluga whale (in lbs) follows a normal distribution with a mean of 132 and a standard deviation of 10. Suppose we obtain a sample of 5 baby beluga whales on a trip to the pute the following P(x<140)Compute the following P(x>143.25)The lifespan for a household hedgehog (in years) is modeled using a normal curve and has a mean of 3 years with a standard deviation of 1.1 years. Suppose we obtain a sample of 20 hedgehogs.What is the probability that the sample mean will be greater than 4.7 years?What is the probability that the sample mean will be less than 2.3 years? ................
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