Scores on a test follow normal distribution with mean of 460 and SD of 100. If all students in class of 41 attend the test what is probability that the given class will obtain a mean score of above 589.93? I can work out the Z score but am confused by the second part of the question. Do i need to work out T-score too ?

ohgodamnitw0

ohgodamnitw0

Answered question

2022-09-03

Scores on a test follow normal distribution with mean of 460 and SD of 100. If all students in class of 41 attend the test what is probability that the given class will obtain a mean score of above 589.93? I can work out the Z score but am confused by the second part of the question. Do i need to work out T-score too ?

Answer & Explanation

Brendan Bradley

Brendan Bradley

Beginner2022-09-04Added 11 answers

The distribution of mean scores follows a N ( 460 , 100 41 ) distribution. Convert 589.93 to a Z score with respect to this distribution (call this z-score z = 589.93 460 100 / 41 ), and then calculate the probability a standard normal is above this z:
P ( Z z ) = 1 P ( Z z ) = 1 Φ ( 589.93 460 100 / 41 )

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