SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on the data from the College Board ATP). If a sample of 15 students is selected randomly, find the probability that the sample mean is above 500. Does the central limit theorem apply for this problem?

The value is  

Step-by-step explanation:

From the question we are told that

       The mean is  

       The standard deviation is  

       The sample size is  n  =  15

Generally  the probability that the sample mean is above 500

Gnerally the standard error of mean is mathematically represented as

=>          

=>          

Generally  the probability that the sample mean is above 500

=>    

From the z table  the area under the normal curve to the right  corresponding to  2.259  is

=>      

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step-by-step explanation: