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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 73 students will have an average score between 970 and 1010? Round your answer to 3 decimal places.

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

mean = = 1000

standard deviation = = 200

= / n = 200 / 73 = 23.4082

= P[(970 - 1000) / 23.4082 < ( - ) / < (1010 - 1000) / 23.4082)]

= P(-1.28 < Z < 0.43)

= P(Z < 0.43) - P(Z < -1.28)

= 0.6664 - 0.1003

= 0.566

Probability = 0.566

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