Assume that SAT scores are normally distributed with mean mu equals 1518 and standard deviation sigma equals 325. If 1 SAT score is randomly selected, find the probability that it is greater than 1600. If 81 SAT scores are randomly selected, find the probability that they have a mean greater than 1600.

And we can find this probability using the z score formula and the complement rule and we got:

And we can find this probability using the z score formula and the complement rule and we got:

Step-by-step explanation:

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

Where and

We want to find this probability:

And we can use the z score formula given by:

Using this formula we got:

And we can find this probability using the z score formula and the complement rule and we got:

For the other part we need to take in count that the distribution for the sampel mean if the sample size is large (n>30) is given by:

And we can use the z score formula given by:

And replacing we got:

And we can find this probability using the z score formula and the complement rule and we got:

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step-by-step explanation:

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