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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 36 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 = 36

=   = 1000

= / n = 200 / 36 = 33.33

P(970 < < 1010)  

= P[(970 - 1000) / 33.33 < ( - ) / < (1010 - 1000) / 33.33 )]

= P(- 0.90 < Z < 0.30)

= P(Z < 0.30) - P(Z < - 0.90)

Using z table,  

= 0.618 - 0.184

= 0.434

orchestra answered 2 years ago
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