According to a study, the time between taking a pain reliever and getting relief of a randomly selectedpatient is normally distributed with a mean of 33 minutes and a standard deviation of 5.2 minutes. Let Xbe the time between taking a pain reliever and getting relief for a randomly selected patient and let Xbe the average time between taking a pain reliever and getting relief for a random sample of size 16.1. Describe the probability distribution of X and state its parameters μ and o:or (μ =33✔ 0 O = 5.✔ Oand find the probability that the time between taking a pain reliever and getting relief for a randomlyselected patient is between 30 and 33 minutes.(Round the answer to 4 decimal places)X~ N2. Use the Central Limit Theoremthe original population is normally distributed although the sample size is small (n<30)to describe the probability distribution of X and state its parameters µ and σx: (Round the answers to1 decimal place)(μX =and find the probability that the average time between taking a pain reliever and getting relief for asample of 16 randomly selected patients is between 33 and 34 minutes.(Round the answer to 4 decimal places)X Nox =

Here random variable X has normal distribution with mean of 33 and standard deviation of 5.2 We…

Answered: According to a study, the time between…

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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A study shows in a certain school that the average number of hours a student answers his/her module in a day is 26.8 hours with a standard deviation of 5.57. Assuming that the data are normally distributed. Find the probability that the number of hours spent by a student in answering his/her modules is between 19 hours and 28 hours. With Normal Curve Distribution representation.
A random variable has a longnormal distribution with mean 10 and variance 4. Calculate the probability that the variable will take a value between 7.5 and 12.5
Let x be a random variable that represents the commute time of teachers in a large rural area. If x is normally distributed with a mean of 64 minutes and a standard deviation of 12.2 minutes, find the probability that a commute time is greater than 70 minutes.
A prototype automotive tire has a design life of 38,500 miles with a standard deviation of 2,500 Five such tires are manufactured and tested. On the assumption that the actual population mean is 38,500 miles and the actual population standard deviation is 2,500 miles, find the probability that the sample mean will be less than 35,000 miles. Assume that the distribution of lifetimes of such tires is normal. A normally distributed population has mean 1,200 and standard deviation Find the probability that a single randomly selected element X of the population is between 1,100 and 1,300. Find the mean and standard deviation of X for samples of size Find the probability that the mean of a sample of size 25 drawn from this population is between 1,100 and 1,300. Scores on an entrance exam in a large university, freshman course are normally distributed with mean 72.5 and standard deviation 13.0. Find the probability that the score X on a randomly selected exam paper is between 70…
Two devices are used to measure the length of beam. If the true length of the beam is L, the measurement error made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L, and the measurement error made by the other device, E, , is normally distributed with mean 0 and standard deviation 0.004L. The two measurement errors are independent of each other. What is the probability that the average value of the two measurements, (E, + E,)/2, is within 0.5% of L? Note that this problem can be done using the attached table of the cdf of the standard normal random variable.
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
In a factory production the products' weights follow a normal distribution with mean 4.00 kg and standard deviation 0.06 kg. Suppose a product is chosen at random, find the probability that the product's weight is between 3.88 kg and 4.18 kg?
The lifetime of a particular component is normally distributed, with a mean of 1000 hours, and a standard deviation of 100 hours. Find the probability that a randomly-drawn component will last 930 hours or less.
You studied a third CPU and found that its speed is a continuous random variable that follows a normal distribution, with a mean value of 3.6 GHz and a standard deviation of 0.8 GHz. Find the probability that the third CPU would run faster than the expected speed of CPU1.

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