### 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

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A die was rolled 360 times and the results were: No. of Spots (outcomes) Frequency 1 54 2 70 3 58 4 62 5 50 6 66 Is the die balanced at a = 0.05? Determine the test statistic to be used. O A. Chi-square test B. z-Test O C. t-Test O D. F-test
Which of the following formulas is used to calculate the standard deviation of the sampling distribution of the sample mean (for infinite population) when the population standard deviation is given? A. 0g N-n C. Oz= N-n %3D VN-1 Vn+1 V N-1 B. 0 D. Og = 5.
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r:32. Compute the median weight of the rabbits from the following data: Serial Number: 1 3 4 Weight in gms: 120 150 110 190 160 95.

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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.