Note: Make sure that your calculator is set to degree mode. The figure below shows a sketch of
⊙
N
with equation
(
x
−
2
)
2
+
(
y
+
1
)
2
=
169
4
. The chord
¯¯¯¯¯¯
A
B
in
⊙
N
is parallel to the
x
-axis, lies below the
x
-axis and has a length of 12 units.
¯¯¯¯¯¯
A
P
and
¯¯¯¯¯¯
B
P
are tangent to
⊙
N
and intersect at point
P
.

pic

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?