3The median value y of a continuous random variable is that value such that F(y) = 0.5. Find the median value of the random variable in90.5=f(y) =225-Y, 0 ≤ y ≤ 5,elsewhere.0,

The median value of continuous random variables is that value such that The PDF of is given as,

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A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The distribution of certain test scores is a nonstandard normal distribution with a mean of 80 and a standard deviation of 9. What are the values of the mean and a standard deviation after all test scores have been standardized by converting them to z-scores using z=(x-µ)/σ? A) The mean is 100 and the standard deviation is 10 B) The mean is 0 and the standard deviation is 1 C) The mean is 1 and the standard deviation is 0 D) The mean is 10 and the standard deviation is 100
X~ N(10,12). Suppose that you form random samples of 16 from this distribution. Let be the random variable of averages. Let EX be the random variable of sums. Round all answers to two decimal places. A. ~ N( B. P( 150) =
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Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. (a) In words, define the random variable X. Edit Insert Formats BIUX₂ + 2+ 3 = C P & (b) Find the z-score for a trial lasting 19 days. your answer to three decimal places.) Shade: Left of a value (c) If one of the trials is randomly chosen, find the probability that it lasted at least 19 days. +||||||||| (d) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (b), rounded to one decimal place). -1 X² A ▾ A▾ -1.5 用 Σ+ Σ Α 2 Click and drag the arrows to adjust the values. (Round ++++++++++++ 3 4 (e) eighty-eight percent of all trials of this type are completed within how many days?
The distribution function for a random variable X is F (x) = {-e-", 20 x > 0 to x 2? e 2 e -5 -4 e
A standardized exam’s score are normally distributed. In a recent year, the mean test score was 1477 and the standard was 315. The test scores of four students selected at random 1860 1230, 2160, and 1360. Find the Z- score that correspond to each value and determine wether any of the values are unusual. The Z-score for 1860 is-The Z-score for 1230 is-The Z-score for 2160 is-The Z-score for 1360is-
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Suppose that f(x)=2/(3^x), x=1,2,3,... is the probability function for a random variable X. Find P(X>3). Use 4 decimal places.
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X ~ N(60, 14). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums.Give the distribution of X. Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(X < 60) =.Find the 30th percentile.
Q7) The length of time, in seconds, that a computer user takes to read his or her e- mail is distributed as lognormal random variable with μ = 1.8 and o² = 4. (a) (b) What is the probability that a user reads e-mail for more than 20 seconds? More than a minute? What is the probability that a user reads e-mail for a length of time that is equal to the mean of the underlying lognormal distribution?

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3 The median value y of a continuous random variable is that value such that F(y) = 0.5. Find the median value of the random variable in -{ 40.5 = f(y) = 2 -Y, 0 ≤ y ≤ 5, elsewhere. 25 0,