b Calculate the probability that X is greater than 56 and less than 80 c If you

B calculate the probability that x is greater than 56

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b) Calculate the probability that X is greater than 56 and less than 80. c) If you obtained a random sample of size n = 20 from the population of X described above, what would be the probability that the sample variance, s 2 , is greater than 30? d) Imagine a symmetric interval around the mean (μ ± c) of the distribution described above. Find the value of c such that the probability is about 0.2 that X is in this interval.
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Question 3 – A Density Function A random variable X has the following density function a) Draw the density function of X. b) Show that the function above has the necessary characteristics to be a density function. c) Calculate the probability that X takes a value between 0.6 and 1. d) Find the probability that X takes a value between 0.5 and 1.25. Question 4 – Coin Flips Suppose you throw a coin four times. For each "head", you receive one point, and for each "tail", you lose one point. a) Develop the sampling distribution for the average number of points you receive for throwing four coins. (Use a table) b) What is the standard deviation for the sampling distribution? c) What is the probability that the average number of points you receive after four throws is 0.5? d) What is the probability that the average number of points you receive on four casts is 0? Question 5 – Exponential Distribution Using the density function of the exponential distribution, show that the cumulative distribution function of a random variable following an exponential distribution is F(t)=1-e - λ t
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