![]() Suppose one wishes to find the $x$ value for which a normally distributed random variable with mean $\mu$ and standard deviation $\sigma$ will produce an outcome less than $x$ with some given probability of $p$. The last argument for this function, when $TRUE$, indicates the function should return should cumulative probability equal to the area under the associated normal curve to the left of $x$ (as opposed to the height of the function). Notice, in the last example, we find the area under the normal curve between $x=a$ and $x=b$ by finding a difference of two left-tailed areas. Under the same assumptions, what is the probability that a selected packet has a weight within 2 standard deviations of the mean weight? What is the probability that a selected packet is less than $78$ grams? Suppose the manufacturer of a certain type of snack knows that the total weight of the snack packet they sell is normally distributed with a mean of $80.2$ grams and a standard deviation of $1.1$ grams. the area under the normal curve to the left of $x$.), To find the probability that a normally distributed random variable with mean $\mu$ and standard deviation $\sigma$ results in a value less than $x$ (i.e. The last argument for this function, when $FALSE$, indicates that the height of $f(x)$, not a cumulative probability, should be returned. ![]() ![]() To find this value (i.e., the height of $f$ at $x$),Īs an example, the height at $x=13$ of the normal curve with mean 10 and standard deviation 7 is given by Recall that a normal distribution with mean $\mu$ and standard deviation $\sigma$ is one characterized by the function: Tech Tips: Normal Distributions Calculating Heights of a Normal Curve
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