The following data resulted from 15 independent measurements of the melting point of lead. 322.3 339.1 323.3 330.8 328.4 323.2 338.3 324.2 334.9 328.2 329.4 329.5 328.2 339.7 326.5 assuming that the measurements can be regarded as constituting a normal sample whose mean is the true melting point of lead, determine a 95% confidence interval for this value.

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Jenisey has $24 to spend on seven pencils. after buying them she had $10. how much did each pencil cost.?

Jack did 3/5 of all problems on his weekend homework before sunday. on sunday he solved 1/3 of what was left and the last 4 problems. how many problems were assigned for the weekend?