Here we are dealing with the t-distribution.

t=(mu-m)/(s/sqrt(n))

has a t-distribution with n-1 degrees of freedom. The 90% confidence region

for t with 16 degrees of freedom is:

(-1.75, 1/75),

or for mu:

(-1.75 s/sqrt(n) + m, 1.75 s/sqrt(n) + m) = (-1.75x583/sqrt(17)+m, 1.75x583/sqrt(17)+m)

...................= (-247.446+m, 247.466+m)

But we are told that the upper end point is 525.9, so:

525.9=247.466 + m,

so m=278.434, and so the lower end of the interval is: 30.968, or rounding

to 1 decimal place: 31.0.

RonL