Question

The scores of students on the SAT college entrance examinations at a certain high school had...

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean ?=531.7 and standard deviation ?=25.5

consider a simple random sample (SRS) of 30 students who took the test.

The standard deviation of the sampling distribution for ?¯ is?

What is the probability that the mean score ?¯ of these students is 536 or higher?

Math   Statistics-And-Probability   
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Answer #1

Solution :

The standard deviation of the sampling distribution for ?¯ is

= / n = 25.5 / 30 = 4.6556

P( 536) = 1 - P( 536)

= 1 - P[( - ) / (536 - 531.7) / 4.6556]

= 1 - P(z 0.924)

= 0.1777

Probability = 0.1777

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