Almost all medical schools require applicants to take the Medical College Admission Test (MCAT). Scores on the MCAT are approximately Normal with a mean of 25 and a standard deviation of 6.5. To estimate the mean score of WSSU students who took the MCAT, the School of Health Sciences obtains an SRS of scores 10 students. What is the probability that this sample will have an average score between 23 and 26? Almost all medical schools require applicants to take the Medical College Admission Test (MCAT).

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Almost all medical schools require applicants to take the Medical College Admission Test (MCAT).

Scores on the MCAT are approximately Normal with a mean of 25 and a standard deviation of 6.5. To estimate the mean score of WSSU students who took the MCAT, the School of Health Sciences obtains an SRS of scores 10 students. What is the probability that this sample will have an average score between 23 and 26?

Almost all medical schools require applicants to take the Medical College Admission Test (MCAT).

 

Expert Solution
Step 1

Obtain the probability that this sample will have an average score between 23 and 26.

 

The probability that this sample will have an average score between 23 and 26 is obtained below as follows:

 

Let X denotes the scores on the MCAT which follows normal distribution with the mean of 25 inch and the standard deviation of 6.5 with the sample 10 students has been randomly selected.

 

Since the population distribution is normally distributed the sample mean of the sampling distributed also follows normal distribution.

That is, the mean of the sampling distribution is,

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