Question

For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of

515

and a standard deviation of

170

. The grading process of this year's exam has just begun. The average score of the

40

exams graded so far is

490

. What is the probability that a sample of

40

exams will have a mean score of

490

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.

Answer 1

Solution :

mean = = 515

standard deviation = = 170

n = 40

= = 515

= / n = 170 / 40 = 26.8794

P( > 490) = 1 - P( < 490)

= 1 - P[( - ) / < (490 - 515) / 26.8794]

= 1 - P(z < -0.93)

Using z table,    

= 1 - 0.176

= 0.824