Solution: From 68-95-99.7 rule, we know that in normal distribution 95 percent of data comes under 2-standard deviation.Mean of the data = Problem 2: If mean of a given data for a random value is 81.1 and standard deviation is 4.7, then find the probability of getting a value more than 83.Solution: Standard deviation, $\sigma$ = .7$Mean, Mean $\mu $ = 81.1Expected value, X = 83Z-score, $z$ = Problem 3: The average speed of a car is 65 kmph with a standard deviation of 4.Tags: Essay AnalysingAcquainted With The Night Analysis EssayReferences In Research PaperReflective Essay On Waiting For SupermanMarketing Management AssignmentGood Persuasive Research Paper TopicsPitt University Application Essay
A positive Z-score refers to a standard deviation that is to the right of the mean, meaning that it is greater than the mean.
On the other hand, a negative Z-score refers to a standard deviation that is to the left of the mean, meaning that it is less than the mean.
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Try it risk-free In this lesson, we will put the normal distribution to work by solving a few practice problems that help us to really master all that the distribution, as well as Z-Scores, have to offer. If you've been working with normal distributions for long, you've probably figured out that they are pretty useful things.
Before we delve too deep into using the normal distribution, let's be sure that we are squared away on how it works first.
The highest point of the curve is where the mean is located.The formula for that is simple - take the value of the point in question, subtract the mean from it, then divide it by the standard deviation.z = (data point - mean) / standard deviation Sometimes you'll have negative Z-scores. Whereas a positive Z-score means that a Z-score represents a value greater than the mean, a negative Z-score just means the represented value is less than the mean.Solution: Mean $\mu$ = 65Standard deviation, $\sigma$ = 4Expected value, X = 4Z-score, $z$ = Problem 4: The average score of a statistics test for a class is 85 and standard deviation is 10.Find the probability of a random score falling between 75 and 95.Besides that, statisticians needed some form of common ground to develop tests and techniques.For example, the proofs of many hypothesis tests are based on the assumption that the sample is normally distributed.In practice, normal distribution is used almost everywhere, from cancer tests to production lines.Rarely we observe false use of normal distribution in applied statistics, but it is impossible to be applied in real life situations (e.g. It’s worth mentioning that standard normal distribution is a special case of normal distribution where the mean is zero and the standard deviation one.Normal distribution is a symmetric distribution where the single peak is at the mean of the data.The normal distribution curve is bell shaped and the spread of data is controlled by the standard deviation.