MATH 533 Week 8 Final Exam Set 3
Answer The length of time to do a cable installation by
Multi-Cable Inc. is normally distributed with a mean of 42.8
minutes & a standard deviation of 6.2 minutes. What
percentage of installations take less than 30 minutes?
x = The length of time to do a cable installation
= 42.8
= 6.20
x-
z=
P(x < 30)
= P(z < -2.06)
= 0.5 - 0.4803
= 0.0197 or 1.97%
, MATH 533 Week 8 Final Exam Set 3
Answer Accident claims are checked for completeness by
branch offices of Fortune Insurance before they are sent to
a regional office for payment. Historically 80% of the
claims are complete when they reach the regional office.
You select a random sample of 20 claims that have arrived at
the regional office. Find the probability that:
X = Number of completed forms in sample
n = 20
p = 0.80
a. At least 16 claims are complete,
P(X 16) = P(X = 16) + … + P(X = 20)
= 0.6296
b. All 20 are complete,
P(X = 20) = 0.0115
c. Fewer than 12 are complete,
P(X < 12) = P(X 11) = P(X = 0) + … + P(X =
11)
= 0.0100
d. Exactly 12 are complete.
P(X = 12) = 0.0222
, MATH 533 Week 8 Final Exam Set 3
Answer Until this year the mean braking distance of a Nikton automobile moving at 60
miles per hour was 175 feet. Nikton engineers have developed what they consider a better
braking system. They test the new brake system on a random sample of 81 cars &
determine the sample mean braking distance. The results are:
x = 167 feet s = 27 feet
a. Compute the 90% confidence interval for the mean
braking distance. Interpret this interval.
s
x z𝛼 ( )
n
2
27
167 (1.645)( )
81
167 4.935
162.1 171.9
We are 90% confident that the population mean breaking distance
is between 162.1 ft & 171.9 ft.
b. How many cars should be tested if Nikton wants to be 90%
confident of being within 2 feet of the population mean
braking distance? Assume the sample size will be larger than
30.
( z 𝛼 )2
2
(1.645)2 (27 )2
n = 2
= = 493.17 = 494
2 (2 )
B 2
Answer The length of time to do a cable installation by
Multi-Cable Inc. is normally distributed with a mean of 42.8
minutes & a standard deviation of 6.2 minutes. What
percentage of installations take less than 30 minutes?
x = The length of time to do a cable installation
= 42.8
= 6.20
x-
z=
P(x < 30)
= P(z < -2.06)
= 0.5 - 0.4803
= 0.0197 or 1.97%
, MATH 533 Week 8 Final Exam Set 3
Answer Accident claims are checked for completeness by
branch offices of Fortune Insurance before they are sent to
a regional office for payment. Historically 80% of the
claims are complete when they reach the regional office.
You select a random sample of 20 claims that have arrived at
the regional office. Find the probability that:
X = Number of completed forms in sample
n = 20
p = 0.80
a. At least 16 claims are complete,
P(X 16) = P(X = 16) + … + P(X = 20)
= 0.6296
b. All 20 are complete,
P(X = 20) = 0.0115
c. Fewer than 12 are complete,
P(X < 12) = P(X 11) = P(X = 0) + … + P(X =
11)
= 0.0100
d. Exactly 12 are complete.
P(X = 12) = 0.0222
, MATH 533 Week 8 Final Exam Set 3
Answer Until this year the mean braking distance of a Nikton automobile moving at 60
miles per hour was 175 feet. Nikton engineers have developed what they consider a better
braking system. They test the new brake system on a random sample of 81 cars &
determine the sample mean braking distance. The results are:
x = 167 feet s = 27 feet
a. Compute the 90% confidence interval for the mean
braking distance. Interpret this interval.
s
x z𝛼 ( )
n
2
27
167 (1.645)( )
81
167 4.935
162.1 171.9
We are 90% confident that the population mean breaking distance
is between 162.1 ft & 171.9 ft.
b. How many cars should be tested if Nikton wants to be 90%
confident of being within 2 feet of the population mean
braking distance? Assume the sample size will be larger than
30.
( z 𝛼 )2
2
(1.645)2 (27 )2
n = 2
= = 493.17 = 494
2 (2 )
B 2
