The mean room and board expense per year at fouryear college

The mean room and board expense per year at four-year colleges is $7540. You randomly select 9 four-year colleges. What is the probability that the mean room and board is less than $7800? Assume that the room and board expenses are normally distributed with a standard deviation of $1245.

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Solution

The mean room and board expense per year at four-year colleges is $7540. You randomly select 9 four-year colleges. What is the probability that the mean room and board is less than $7800? Assume that the room and board expenses are normally distributed with a standard deviation of $1245.

Standard error = 1245 /sqrt(9) =415

Z value for 7800,   z= (7800-7540)/415 =0.6265    =0.63( 2 decimals)

P( x <7800) = p( z < 0.63) = 0.7357