Question

The mean room and board expense per year of four-year colleges is $6900.You randomly select 16 four-year colleges. What is the probability that the mean room and board is less than $7500? Assume that the room and board expenses are normally distributed, with a standard deviation of $1000.

Answer 1

Solution:

X: Number of room and board expense per year of four-year colleges is $6900.You randomly select 16 four-year colleges. What is the probability that the mean room and board is less than $7500? Assume that the room and board expenses are normally distributed, with a standard deviation of $1000.

µ = $6900
σ = $1000

n = 16

P(the mean room and board is less than $7500) = P ( x̄ < $7500 )

= P ( (x̄-µ)/(σ/√n) < (7500-6900)/(1000/√16)

= P ( z < 2.40 )

= 0.9918

Answer : 0.9918