Use Minitab to calculate the following probabilities. You must show the Minitab
ID: 3230468 • Letter: U
Question
Use Minitab to calculate the following probabilities. You must show the Minitab output to receive full credit.
a. (4 pts) You make pacemaker leads with an insulating coating. Your process makes pacemaker leads that have a normally-distributed coating thickness with a mean of 2 mm and a standard deviation of 0.1 mm. What is the probability that the lead thickness will be 2.0 ± 0.1 mm?
b. (4 pts) Suppose the customer accepts 80% of your pacemaker leads. What is the probability that the customer would accept at least 18 of the next 20 pacemaker leads that you produce?
c. (4 pts) Your process produces pacemaker leads at an average rate of 1 every 3 seconds. What is the probability that you could produce more than 12 leads in 30 seconds?
please show minitab output!!
Explanation / Answer
Answer:
Use Minitab to calculate the following probabilities. You must show the Minitab output to receive full credit.
a. (4 pts) You make pacemaker leads with an insulating coating. Your process makes pacemaker leads that have a normally-distributed coating thickness with a mean of 2 mm and a standard deviation of 0.1 mm. What is the probability that the lead thickness will be 2.0 ± 0.1 mm?
Cumulative Distribution Function
Normal with mean = 2 and standard deviation = 0.1
x P( X x )
1.9 0.158655
2.1 0.841345
P( 1.9<x<2.1) = P( x <2.1)-P( x <1.9)
=0.841345-0.158655
=0.68269
b. (4 pts) Suppose the customer accepts 80% of your pacemaker leads. What is the probability that the customer would accept at least 18 of the next 20 pacemaker leads that you produce?
Cumulative Distribution Function
Binomial with n = 20 and p = 0.8
x P( X x )
17 0.793915
P( x 18) =1-P( x17) =1-0.793915
=0.206085
c. (4 pts) Your process produces pacemaker leads at an average rate of 1 every 3 seconds. What is the probability that you could produce more than 12 leads in 30 seconds?
average rate of 1 every 3 seconds
for 30 seconds, average rate= 10
Poisson distribution used.
Cumulative Distribution Function
Poisson with mean = 10
x P( X x )
12 0.791556
P( x >12) =1-P( x12) =1-0.791556
=0.208444
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