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Sonbull [250]
3 years ago
9

Suppose that the mean score on a creativity test is 16 and the standard deviation is 4. You are told that the distribution is no

rmal. Using the approximations for normal curves, how many people would get a score between 12 and 20?
Mathematics
1 answer:
Savatey [412]3 years ago
5 0

Answer:

P(12

And we can find this probability on this way:

P(-1

We expect around 68.27% between the two scores provided.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(16,4)  

Where \mu=16 and \sigma=4

We are interested on this probability

P(12

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(12

And we can find this probability on this way:

P(-1

We expect around 68.27% between the two scores provided.

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