### Normal Distribution in Test Scores**Problem Statement:**Suppose test scores are measured by the Gaussian Normal Distribution $ N(X, 75, 10) $. Calculate the following:#### Tasks:**a)** $Pr(80 < X < 90)$**b)** $Pr(50 < X < 70)$**c)** The 95th percentile---In this problem, the Gaussian Normal Distribution has a mean ($\mu$) of 75 and a standard deviation ($\sigma$) of 10. The tasks involve calculating probabilities and the percentile for given test scores.To solve these problems, we'll need to convert raw scores (X) to Z-scores and then use Z-tables or statistical software to find the required probabilities and percentiles.

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Answered: 3) Suppose test scores are measured by…

3) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X< 70) c) The 95 th percentile

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

### Normal Distribution in Test Scores

**Problem Statement:**

Suppose test scores are measured by the Gaussian Normal Distribution $ N(X, 75, 10) $. Calculate the following:

#### Tasks:

**a)** $Pr(80 < X < 90)$

**b)** $Pr(50 < X < 70)$

**c)** The 95th percentile

---

In this problem, the Gaussian Normal Distribution has a mean ($\mu$) of 75 and a standard deviation ($\sigma$) of 10. The tasks involve calculating probabilities and the percentile for given test scores.

To solve these problems, we'll need to convert raw scores (X) to Z-scores and then use Z-tables or statistical software to find the required probabilities and percentiles.

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