Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 20 minutes. A researcher observed 50 students who entered the library to study. Round all answers to 4 decimal places where possible. Suppose that the amount of time that students spend studying in the library in one sitting is normallydistributed with mean 45 minutes and standard deviation 20 minutes. A researcher observed 50 studentswho entered the library to study. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X - N(b. What is the distribution of I? ã - N(c. What is the distribution of > x? )d. If one randomly selected student is timed, find the probability that this student's time will bebetween 44 and 46 minutes.e. For the 50 students, find the probability that their average time studying is between 44 and 46minutes.f. Find the probability that the randomly selected 50 students will have a total study time more than2400 minutes.g. For part e) and f), is the assumption of normal necessary? O NoO Yesh. The top 20% of the total study time for groups of 50 students will be given a sticker that says "Greatdedication". What is the least total time that a group can study and still receive a sticker?minutes

Answered: Suppose that the amount of time that…

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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Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 20 minutes. A researcher observed 50 students who entered the library to study. Round all answers to 4 decimal places where possible.

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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The normal distribution is the most useful theoretical distribution for continuous variables. For the normal distribution,

$m e a n = μ, S . D = σ$ , symbolically we write,

$X ~ N (μ, σ)$ .

The normal curve is always bell-shaped curve.

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