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MATH 533 Week 8 Final Exam Set 3 (100% CORRECT Solution) | Already graded A+ $17.49
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MATH 533 Week 8 Final Exam Set 3 (100% CORRECT Solution) | Already graded A+ MATH 533 Week 8 Final Exam Set 3 (100% CORRECT Solution) | Already graded A+

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  • January 30, 2022
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  • 2021/2022
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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

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