According to a study, the time between taking a pain reliever and getting relief for a randomly selected patient has unknown distribution with a mean of 42 minutes and a standard deviation of 4.5 minutes. Let XX be the time between taking a pain reliever and getting relief for a randomly selected patient and let ¯¯¯XX¯ be the average time between taking a pain reliever and getting relief for a random sample of size 33. 1. Describe the probability distribution of XX and state its parameters μμ and σσ: X~X~ Select an answer B ? χ² N F T ( μ=μ= , σ=σ= ) and find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is less than 50 minutes. (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem Select an answer the original population is normally distributed although the sample size is small (n<30) the sample size is large (n>30) although the distribution of the original populaiton is unknown the original population is normally distributed and the sample is large (n>30) the sample size is small (n<30) and the distribution of the original population is unknown to describe the probability distribution of ¯¯¯XX¯ and state its parameters μ¯¯¯XμX¯ and σ¯¯¯XσX¯: (Round the answers to 1 decimal place)

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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According to a study, the time between taking a pain reliever and getting relief for a randomly selected patient has unknown distribution with a mean of 42 minutes and a standard deviation of 4.5 minutes. Let XX be the time between taking a pain reliever and getting relief for a randomly selected patient and let ¯¯¯XX¯ be the average time between taking a pain reliever and getting relief for a random sample of size 33.

1. Describe the probability distribution of XX and state its parameters μμ and σσ:

X~X~ Select an answer B ? χ² N F T ( μ=μ= , σ=σ= )

and find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is less than 50 minutes.

(Round the answer to 4 decimal places)

2. Use the Central Limit Theorem

Select an answer the original population is normally distributed although the sample size is small (n<30) the sample size is large (n>30) although the distribution of the original populaiton is unknown the original population is normally distributed and the sample is large (n>30) the sample size is small (n<30) and the distribution of the original population is unknown

to describe the probability distribution of ¯¯¯XX¯ and state its parameters μ¯¯¯XμX¯ and σ¯¯¯XσX¯: (Round the answers to 1 decimal place)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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