### Understanding Z-Scores in a Normal DistributionA **normal distribution** is a continuous probability distribution for a random variable, where the data tends to cluster around a mean (average). The shape of the distribution is symmetric and bell-shaped.When dealing with normal distributions, a **z-score** helps us understand how far a particular value (or "x value") is from the mean of the distribution. The formula for calculating the z-score is:\[ z = \frac{{x - \mu}}{{\sigma}} \]where:- \( x \) is the value in question- \( \mu \) is the mean of the distribution- \( \sigma \) is the standard deviation of the distributionGiven a normal distribution with a mean (\( \mu \)) of 40 and a standard deviation (\( \sigma \)) of 4.6, find the z-score for each x value provided. Round all answers to two decimal places.**Problem Set:****a.) Find the z-score corresponding to \( x = 37 \).**\[ \boxed{} \]**b.) Find the z-score corresponding to \( x = 42 \).**\[ \boxed{} \]In these problems:- You need to substitute the given values into the z-score formula.- For example, for part (a), substitute \( x = 37 \), \( \mu = 40 \), and \( \sigma = 4.6 \) to find the z-score.- Compute the value and round to two decimal places.Ensure you perform the calculations carefully and round off your final answers properly as instructed.

Answered: - Given a normal distribution with a μ…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

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- Given a normal distribution with a μ = 40 and o u 4.6 find the z-score that corresponds to each x value below. Round all answers to two decimal places. a.) Find the z-score corresponding to x = 37. b.) Find the z-score corresponding to x = 42.