Question

A mean undergraduate cost for tuition, fees, room, and board for four-year institutions was $26,489 for...

A mean undergraduate cost for tuition, fees, room, and board for four-year institutions was $26,489 for a recent academic year. Suppose that the population standard deviation equals $3,204 and 36 four-year institutions are randomly selected.

Find the probability that the sample mean cost for these 36 schools is between $25,000 and $26,000.

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

mean = = $26489

standard deviation = = $3204

= / n = 3204 / 34 =534

= P[(25000 - 26489) / 534< ( - ) / < (26000 - 26489) /534 )]

= P(-2.79 < Z < -0.92)

= P(Z < -0.92) - P(Z < -2.79)

= 0.1788 - 0.0026 = 0.1762

Probability = $0.1762

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