For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 520 and a standard deviation of 180. The grading process of this year's exam has just begun. The average score of the 35 exams graded so far is 518. What is the probability that a sample of the 35 exams will have a mean score of 518 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

the probability that a sample of the 35 exams will have a mean score of 518 or more is 0.934 or 93.4%.

Step-by-step explanation:

This is s z-test because we have been given a sample that is large (greater than 30) and also a standard deviation. The z-test compares sample results and normal distributions. Therefore, the z-statistic is:

(520 - 518) / (180/√35)

= 0.0657

Therefore, the probability is:

P (X ≥ 0.0657) = 1 - P (X < 0.0657)

where

X is the value to be standardised

Thus,

P (X ≥ 0.0657) = 1 - (520 - 518) / (180/√35)

= 1 - 0.0657

= 0.934

Therefore, the probability that a sample of the 35 exams will have a mean score of 518 or more is 0.934 or 93.4%.