Given the probability density function f(x)1over the interval 0, 6|, answer the following72question, then find the expected value, the mean, the variance and the standard deviation.a) Question: In the context of probability distributions, are the terms "mean" and "expected value"synonyms?Yes, they are synonyms.O No, they are not synonyms.b) Expected value: E(X) =Round your answer to 3 decimals.c) Expected value of X?:E(X²)Round your answer to 3 decimals.d) Variance:Use either exact answers from previous parts or your roundedvalues to determine the variance. Round your answer to 3 decimals.When showing work, you must show at least the starting point and the end point.

We have given that Probability density function f(x) = 1/ 72 *x2 , 0 < x < 6 Mean=…

Answered: 1 x² over the interval 0, 6|, answer…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let x be a continuous random variable that is normally distributed with a mean of 22 and a standard deviation of 5. Find to 4 decimal places the probability that x assumes a value a. between 26 and 34. Probability = i b. between 18 and 31. Probability i
K Assume that females have pulse rates that are normally distributed with a mean of μ = 76.0 beats per minute and a standard deviation of o= 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute. The probability is (Round to four decimal places as needed.) b. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. OB. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. OC. Since the distribution is of sample means, not…
SAT math scores are normally distributed with the parameters below. μ=500σ=100 What is the probability a randomly selected score is less than 580 points What score separates the highest 15% of scores from the rest?
SAT math scores are normally distributed with μ=500,σ=100. What is the probability a randomly selected score is less than 620 points What score separates the highest 1% of scores from the rest?
SAT math scores are normally distributed with the parameters below. μ=500σ=100μ=500σ=100 What is the probability a randomly selected score is more than 460 points ["", "", "", "", ""] What score separates the lowest 20% of scores from the rest?
K Assume that females have pulse rates that are normally distributed with a mean of μ = 76.0 beats per minute and a standard deviation of o= 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 82 beats per minute. The probability is (Round to four decimal places as needed.) b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 82 beats per minute. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. OB. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size. C. Since the distribution is of individuals, not sample…
A normal distribution with a mean of O and a standard deviation of 1 is called O a probability density function. O a standard normal distribution. O an ordinary normal curve. none of the other statements is correct.
Match the appropriate probability distribution functions shown in column B with the statistic present in column A drawn from a normally distributed population. Statistic Probability Distribution Sample Mean, Known population mean population standard deviation F distribution Sample Mean, Known population mean unknown population standard deviation Chi-square distribution Sample standard deviation Student “t”- distribution Ration of Sample Standard deviations Normal Distribution

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