The sat scores have an average of 1200 with a standard deviation of 120. a sample of 36 scores is selected. what is the probability that the sample mean will be larger than 1224? round your answer to three decimal places.

There is a 11.51% probability that the sample mean will be larger than 1224.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , a large sample size can be approximated to a normal distribution with mean \mu and standard deviation

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

The sat scores have an average of 1200 with a standard deviation of 120. This means that .

A sample of 36 scores is selected. what is the probability that the sample mean will be larger than 1224?

This probability is 1 subtracted by the pvalue of Z when .

By the central limit theorem, we have that:

So

has a pvalue of 0.8849.

This means that there is a 1-0.8849 = 0.1151 = 11.51% probability that the sample mean will be larger than 1224.

b

step-by-step explanation:

can you put the picture up?

step-by-step explanation: