The SAT scores for students are normally distributed with a mean of 1000 and a standard...

The SAT scores for students are normally distributed with a mean of 1000 and a standard deviation of 200. What is the probability that a sample of 45 students will have an average score between 970 and 1010? Round your answer to 3 decimal places.

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Expert Solution

Solution :

Given that ,

mean = = 1000

standard deviation = = 200

n = 45

= 1000

= / $\sqrt$ n= 200/ $\sqrt$ 45=29.81

P(970< < 1010) = P[(970-1000) / 29.81< ( - ) / < (1010-1000) / 29.81)]

= P( -1.01< Z <0.34 )

= P(Z < 0.34) - P(Z <-1.01 )

Using z table

=0.6331-0.1562

=0.4769

probability=0.477

orchestra answered 1 year ago

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