Question

In: Statistics and Probability

The grades on an examination are normally distributed with mean of 400 and standard deviation of...

The grades on an examination are normally distributed with mean of 400 and standard deviation of 40. If a sample 25 students is randomly selected, what is the probability that the average score of these 25 students is above 405?

Expert Solution

Solution :

Given that,

mean = = 400

standard deviation = = 40

n=25

= =400

= / n =40 / 25 = 8

P( >405 ) = 1 - P( <405 )

= 1 - P[( - ) / < (405-400) / 8]

= 1 - P(z <0.625 )

Using z table

= 1 - 0.7340

= 0.2660

probability= 0.2660

orchestra answered 2 years ago

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