Two different box-filling machines are used to fill cereal boxes on the assembly line. The critical measurement influenced by these machines is the weight of the product in the machines. Engineers are quite certain that the variance of the weight of product is
σ
2
=
2
ounces. Experiments are conducted using both machines with sample sizes 100 each. The sample averages for machine A and B are
¯
x
A
=
4.5
ounces and
¯
x
B
=
4.8
ounces. Engineers seemed surprised that the two sample averages for the filling machines were so different.

a. Use the central limit theorem to determine
P
(
¯
X
B
−
¯
X
A
≥
0.3
) under the condition that
μ
A
=
μ
B
.

b. Do the aforementioned experiments seem to, in any way, strongly' support a conjecture that the two population means for the two machines are different? Explain using your answer in (a).