Answered: According to a study, the time between…

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)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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