It is asserted that 70% of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Findthe probability that in a sample of eight cars:PctureவாClick here for the Excel Data Filea All eight will have the transponder. (Round your answer to 4 decimal places.)Frobabilityb. At least three will have the transponder. (Round your answer to 4 decimal places.)Probabilityhave a transponder. (Round your answer to 6 decimal places.)c. None wilProbabilityNext>of 10Prevype here to search

Question
Asked Oct 14, 2019
It is asserted that 70% of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find
the probability that in a sample of eight cars:
Pcture
வா
Click here for the Excel Data File
a All eight will have the transponder. (Round your answer to 4 decimal places.)
Frobability
b. At least three will have the transponder. (Round your answer to 4 decimal places.)
Probability
have a transponder. (Round your answer to 6 decimal places.)
c. None wil
Probability
Next>
of 10
Prev
ype here to search
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It is asserted that 70% of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of eight cars: Pcture வா Click here for the Excel Data File a All eight will have the transponder. (Round your answer to 4 decimal places.) Frobability b. At least three will have the transponder. (Round your answer to 4 decimal places.) Probability have a transponder. (Round your answer to 6 decimal places.) c. None wil Probability Next> of 10 Prev ype here to search

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check_circleExpert Solution
Step 1

Given:

Sample size(n)=8

Probabilty(P)=0.70

Explanation:

Let's x is random variable.

The formula of binomial distribution is:

 

Р(X %3 х)- "С,p" (1-р)"*
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Р(X %3 х)- "С,p" (1-р)"*

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Step 2

The probability that all eight will have the transponder is calculated as follows:

P(X=8)= C, x(0.70) x(1-0.70)
=1x(0.70) x1
*
8
0.0576
==
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P(X=8)= C, x(0.70) x(1-0.70) =1x(0.70) x1 * 8 0.0576 ==

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Step 3

Hence, the probability is 0.0576.

b)

To find the probabilty that at least 3 will have the transponder.

Explanation:

The prob...

P(X23)1-P(X<3)
1-[P(X=0)+P(X= 1)+ P(X =2)]
'c, x(0.7)x (1-0.7)'cx(0.7x(1-0.7)
+C, x(0.7 x(1-0.7)
x1x (1-0.7)+8x (0.7) x (1 - 0.7)
-+28x(0.7)'x(1-0.7)
=1-
=1-
6
=1-0.01129
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P(X23)1-P(X<3) 1-[P(X=0)+P(X= 1)+ P(X =2)] 'c, x(0.7)x (1-0.7)'cx(0.7x(1-0.7) +C, x(0.7 x(1-0.7) x1x (1-0.7)+8x (0.7) x (1 - 0.7) -+28x(0.7)'x(1-0.7) =1- =1- 6 =1-0.01129

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