88 Midterm Quality

1. By means of a scatter diagram, determine if there is a relationship between hours of
machine use and millimeters off the target. Data for 20 pairs with hours of machine
use as x variable are (30, 1,10), (31, 1.21), (32, 1.00), (33, 1.21), (34, 1.25), (35, 1.23),
(36, 1.24), (37, 1.28), (38, 1.30), (39, 1.30), (40, 1.38), (41, 1.35), (42, 1.38), (43, 1.38),
(44,1.40), (45,1.42), (46, 1.45), (47, 1.45), (48, 1.50), and (49, 1.58). Draw a line for
the data using eyesight only and estimate the number of millimeters off the target at 55 hours.

2. A manufacturing process produces thousands of diodes per day. On the average, 1% of
these diodes do not conform to specifications. Every hour, an inspector selects a random
sample of 50 diodes and classifies each diode in the sample as conforming or nonconforming.
Calculate the probability of finding one or less nonconforming parts in the sample.

3. The diameter of a metal shaft used in a disk-drive unit is normally distributed with
mean 0.2508 in. and standard deviation 0.00005 in. The specifications on the shaft have
been established as 0.2500±0.0015 in. Determine the fraction of the shafts produced
conforms to specifications.

4. A manufacturer of electronic calculators offers a one-year warranty. If the calculator fails
for any reason during this period, it is replaced. The time to failure is well modeled by the
following probability distribution:

(b) The manufacturing cost of a calculator is $50, and the profit per sale is $25.
What is the effect of warranty replacements on profit?

5. Surface finish defects in a small electric appliance occur at random with a mean rate
of 0.1 defects per unit. Find the probability that a randomly selected unit will contain at
least one surface finish defect.

6. The diameter of eight automotive piston rings is shown below. Calculate the sample mean,
sample variance, and sample standard deviation.

74.001 mm	74.005	74.003	74.001
73.998 mm	74.000	74.006	74.002