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andrey2020 [161]
3 years ago
11

Use the Statistical Applet: Normal Density Curve to answer the question.Set the mean and standard deviation to 0 and 5 , respect

ively. Note that 0.023 of the area under the curve falls below −10.0 . Now set the mean to 10 and keep the standard deviation at 5 . Under these settings, 0.023 of the area under the curve falls below 0.0 . Proportion?
Mathematics
1 answer:
SVEN [57.7K]3 years ago
4 0

Answer:

z=-1.995

And if we solve for a we got

a=10 -1.995*5=0.025

Step-by-step explanation:

For this case we have the initial case we have a normal distribution given :

X \sim N(0,5)  

Where \mu=0 and \sigma=5

And from the info of the problem we know that:

P(X

We can verify this using the z score formula given by:

z= \frac{x\mu}{\sigma}

And if we replace we got:

P(X

Now we have another situation for a new random variable X with a new distribution given by:

X \sim N(10,5)  

Where \mu=10 and \sigma=5

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.977   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.023 of the area on the left and 0.977 of the area on the right it's z=-1.995. On this case P(Z<-1.995)=0.023 and P(z>-1.995)=0.977

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-1.995

And if we solve for a we got

a=10 -1.995*5=0.025

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