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College Costs The mean undergraduate cost for tuition, fees, room, and board for four-year institutions was $26,489 for a recent academic year. Suppose that o = $3204 and that 36 four-year institutions are randomly selected. Find the probability that the sample mean cost for these 36 schools is a. Less than $25,000 b. Greater than $26,000 c. Between $24,000 and $26,000

User Mazz
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Final answer:

To find the probability for different sample mean costs, we can use the z-score formula. For a sample mean cost less than $25,000, the probability is approximately 0. For a sample mean cost greater than $26,000, the probability is approximately 0.352. And for a sample mean cost between $24,000 and $26,000, the probability is approximately 0.352.

Step-by-step explanation:

To find the probability that the sample mean cost for the 36 schools is less than $25,000, we need to calculate the z-score for this value. The formula to calculate the z-score is:

z = (x - mean) / (o / sqrt(n))

Substituting the given values:

z = (25000 - 26489) / (3204 / sqrt(36))

Simplifying:

z = -2489 / 534 = -4.66

Using a standard normal distribution table or calculator, we can find the probability associated with the z-score of -4.66. This probability is approximately 0.

Therefore, the probability that the sample mean cost for these 36 schools is less than $25,000 is approximately 0.

For part b, we need to calculate the z-score for $26,000 using the same formula. The z-score is:

z = (26000 - 26489) / (3204 / sqrt(36)) = -201 / 534 = -0.38

Using the standard normal distribution table or calculator, we find that the probability associated with a z-score of -0.38 is approximately 0.352.

Therefore, the probability that the sample mean cost for these 36 schools is greater than $26,000 is approximately 0.352.

For part c, we need to calculate the z-scores for $24,000 and $26,000. The z-scores are:

z1 = (24000 - 26489) / (3204 / sqrt(36)) = -2494 / 534 = -4.67

z2 = (26000 - 26489) / (3204 / sqrt(36)) = -201 / 534 = -0.38

Using the standard normal distribution table or calculator, we find that the probability associated with a z-score of -4.67 is approximately 0 and the probability associated with a z-score of -0.38 is approximately 0.352.

Therefore, the probability that the sample mean cost for these 36 schools is between $24,000 and $26,000 is approximately 0.352.

User Wayne Kao
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