Question

In: Statistics and Probability

5. The mean room and board expense per year at four-year colleges is $10,453 and standard...

5. The mean room and board expense per year at four-year colleges is $10,453 and standard deviation $1650. You randomly select 64 four-year colleges.

a. What is the probability that the mean room and board is less than $10,750?

b. What is the probability that the mean room and board is between $9,700 and 10,300?

Solutions

Expert Solution

As the sample size here is 64 > 30, therefore Central limit theorem is applicable here and the distribution of sample mean here is given as:

a) The probability that the mean room and board is less than $10,750 is computed here as:

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

therefore 0.9251 is the required probability here.

b) The probability here is computed as:

Getting it from the standard normal tables, we have here:

Therefore 0.2295 is the required probability here.

orchestra answered 1 year ago
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