According to a study, the time between taking a pain reliever and getting relief of a randomly selected patient is normally distributed with a mean of 38 minutes and a standard deviation of 4.2 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 16. 1. Describe the probability distribution of XX and state its parameters μμ and σσ: X∼X∼ ( 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 between 26 and 47 minutes. (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem to describe the probability distribution of ¯¯¯XX¯ and state its parameters μ¯¯¯XμX¯ and σ¯¯¯XσX¯: (Round the answers to 1 decimal place) ¯¯¯X∼X¯∼ ( μ¯¯¯X=μX¯= , σ¯¯¯X=σX¯= ) and find the probability that the average time between taking a pain reliever and getting relief for a sample of 16 randomly selected patients is less than 38 minutes.
According to a study, the time between taking a pain reliever and getting relief of a randomly selected patient is normally distributed with a mean of 38 minutes and a standard deviation of 4.2 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 16. 1. Describe the probability distribution of XX and state its parameters μμ and σσ: X∼X∼ ( 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 between 26 and 47 minutes. (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem to describe the probability distribution of ¯¯¯XX¯ and state its parameters μ¯¯¯XμX¯ and σ¯¯¯XσX¯: (Round the answers to 1 decimal place) ¯¯¯X∼X¯∼ ( μ¯¯¯X=μX¯= , σ¯¯¯X=σX¯= ) and find the probability that the average time between taking a pain reliever and getting relief for a sample of 16 randomly selected patients is less than 38 minutes.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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According to a study, the time between taking a pain reliever and getting relief of a randomly selected patient is normally distributed with a mean of 38 minutes and a standard deviation of 4.2 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 16.
1. Describe the probability distribution of XX and state its parameters μμ and σσ:
X∼X∼ ( 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 between 26 and 47 minutes.
(Round the answer to 4 decimal places)
2. Use the Central Limit Theorem
to describe the probability distribution of ¯¯¯XX¯ and state its parameters μ¯¯¯XμX¯ and σ¯¯¯XσX¯: (Round the answers to 1 decimal place)
¯¯¯X∼X¯∼ ( μ¯¯¯X=μX¯= , σ¯¯¯X=σX¯= )
and find the probability that the average time between taking a pain reliever and getting relief for a sample of 16 randomly selected patients is less than 38 minutes.
(Round the answer to 4 decimal places)
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