What Is The Probability That None Of These Vehicles Requires Warranty Service?
Question 1118194: Industry standards propose that 16% of new vehicles require warranty service within the first year. Jones Nissan, sold eight Nissans yesterday. (Round the Mean answer to ii decimal places and the other answers to 4 decimal places.)
a. What is the probability that none of these vehicles requires warranty service?
Probability
b. What is the probability that exactly one of these vehicles requires warranty service?
Probability
c. Determine the probability that exactly 2 of these vehicles require warranty service.
Probability
d. What is the probability that less than three of these vehicles require warranty service?
Probability
due east. Compute the mean and standard divergence of this probability distribution.
Mean � =
Standard deviation σ =
Reply by rothauserc(4718)
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Apply the Binomial Probability Distribution Formula
:
Probability (P) (k successes in n trials) = nCk * p^(k) * (i-p)^(due north-g), where nCk = n! / (k! * (n-k)!)
:
For these problems n=8 and p=0.16
:
a) P (one thousand=0) = 8C0 * (0.xvi)^0 * (1-0.16)^(8-0) = 0.2479
:
b) P (1000=1) = 8C1 * (0.xvi)^1 * (1-0.xvi)^(8-ane) = 0.3777
:
c) P (thousand=2) = 8C2 * (0.16)^ii * (1-0.xvi)^(8-2) = 0.2518
:
d) P (k<iii) = P(thou=0) +P(k=ane) +P(k=ii) = 0.2479 +0.3777 +0.2518 = 0.8774
:
e. Compute the mean and standard deviation of this probability distribution
:
mean = 8 * 0.16 = 1.28
:
standard difference = foursquare root(due north * p * (i-p)) = foursquare root(8 * 0.sixteen * (1-0.16)) = 1.0369
:
What Is The Probability That None Of These Vehicles Requires Warranty Service?,
Source: https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1118194.html
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