IDNLearn.com: Your go-to resource for finding expert answers. Whether it's a simple query or a complex problem, our community has the answers you need.
Sagot :
Answer:
26
Step-by-step explanation:
We can work backwards using the z-score formula to find the mean. The problem gives us the values for z, x and σ. So, let's substitute these numbers back into the formula:
z−4−16−2626=x−μσ=10−μ4=10−μ=−μ=μ
We can think of this conceptually as well. We know that the z-score is −4, which tells us that x=10 is four standard deviations to the left of the mean, and each standard deviation is 4. So four standard deviations is (−4)(4)=−16 points. So, now we know that 10 is 16 units to the left of the mean. (In other words, the mean is 16 units to the right of x=10.) So the mean is 10+16=26.
Answer:
[tex]26[/tex] points.
Step-by-step explanation:
Let [tex]X[/tex] denote a normal random variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex]. (That is: [tex]X \sim {\rm N}(\mu,\, \sigma)[/tex].) By definition, the [tex]z[/tex]-score of an observation with value [tex]X = x[/tex] would be:
[tex]\begin{aligned} z&= \frac{x - \mu}{\sigma}\end{aligned}[/tex].
In this question, the value of [tex]\sigma[/tex] is given. Also given are the value of the observation [tex]x[/tex] and the corresponding [tex]z[/tex]-score, [tex]z\![/tex]. Rearrange the [tex]\! z[/tex]-score definition [tex]z = (x - \mu) / \sigma[/tex] to find an expression for [tex]\mu[/tex]:
[tex]\begin{aligned} x - \mu = \sigma\, z\end{aligned}[/tex].
[tex]-\mu = (-x) + \sigma\, z[/tex].
[tex]\begin{aligned}\mu = x - \sigma\, z\end{aligned}[/tex].
Substitute in the value of [tex]x[/tex], [tex]\sigma[/tex], and [tex]z[/tex] to find the value of [tex]\mu[/tex], the mean of this normal random variable:
[tex]\begin{aligned}\mu &= x - \sigma\, z \\ &= 10 - (-16) \\ &= 26\end{aligned}[/tex].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.
