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The SAT scores for students are normally distributed with a mean of 1050 and a standard...

The SAT scores for students are normally distributed with a mean of 1050 and a standard deviation of 205. What is the probability that a sample of 30 students will have an average score between 1030 and 1060? Round your answer to 3 decimal places.

Group of answer choices

0.058

0.309

0.583

0.761

0.691

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution :

Given that,

mean = = 1050

standard deviation = = 205

= / n = 205 / 30 = 37.4277

= P[(1030 - 1050) / 37.4277< ( - ) / < (1060 - 1050) /37.4277 )]

= P(-0.534 < Z < 0.267)

= P(Z < 0.267) - P(Z < -0.534)

= 0.6053 - 0.2967

0.309

Probability = 0.309

Option 2nd is correct.

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