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ective Circuits: Questions 1 – 8 pertain to the table below which show the proba

ID: 3179567 • Letter: E

Question

ective Circuits: Questions 1 – 8 pertain to the table below which show the probability distribution of the number of defects X in a randomly chosen circuit board.

X

P(X)

0

0.50

1

0.30

2

0.10

3

0.10

Does the table above satisfy the requirements for a probability distribution?

(a) Yes (b) No

Find the probability of getting exactly 2 defects?

(a) .10 (b) .30 (c) .50 (d) .20 (e) .40

Find the probability of getting one or more defects?

(a) .30 (b) .40 (c) .50 (d) .60 (e) .20

Find the probability that at least two circuits are defective?

(a) .10 (b) .20 (c) .30 (d) .40 (e) .80

Find the probability that no more than two circuits are defective?

(a) .10 (b) .60 (c) .20 (d) .90 (e) .80

Compute the mean in the probability distribution above?

(a) 0.20 (b) 0.30 (c) 0.10 (d) 0.70 (e) .80

Compute the standard deviation I the probability distribution above.

(a) 0.186 (b) 0.960 (c) 0.980 (d) 0.890 (e) .963

A circuit board will function if it has no defects or only one defect. What is the probability that a circuit board will function?

(a) 0.80 (b) 0.20 (c) 0.60 (d) 0.40 (e) .50

Each of the following is a requirement for a binomial distribution EXCEPT:

A fixed number of trials

Trials must be independent

All outcomes must be classified into 2 or more categories

Probabilities must remain constant for each trial

A question on a proficiency test is multiple choice with five possible answers, one of which is correct.  Assuming that all responses are random guesses, find the probability that among 13 test subjects, at least five answer the question correctly.

(a) .027 (b) .099 (c) .103 (d) .053 (e).901

Rates of on-time flights for commercial jets are continuously tracked by the U.S Department of Transportation.  Recently, Southwest Air had the best rate with 80% of its flights arriving on time.  A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time.  Find the probability that exactly 10 flights arrive on time.

(a) .206 (b) .103 (c) .010 (d) .188 (e) .003

Refer to question 11.  Find the probability that at least 10 flights arrive on time.

(a) .939 (b) .061 (c) .854 (d) .759 (e) .093

Refer to question 11.  Find the probability that at least 5 flights arrive late.

(a) 1.00 (b). 836 (c) .939 (d) .164 (e) .836

Refer to question 11. Find the probability that 7 or fewer flight arrive late.

(a)1.00 (b) .000 (c) .004 (d) .996 (e) .862

Identify whether the given random variable is discrete or continuous.

“The amount of rain during the next thunderstorm”

(a)Discrete (b) continuous

Determine whether the given procedure results in a binomial distribution.

“Five different Senators are randomly selected with replacement from the 100 Senators in the current Congress, and each was asked whether he or she is in favor of abortion.”

(a)Not Binomial (b) Binomial

Explanation / Answer

table above satisfy the requirements for a probability distribution = 0.5+0.3+0.1+01 = 1

the probability of getting exactly 2 defects = 0.1

the probability of getting one or more defects = 0.3 + 0.1 + 0.1 = 0.5

the probability that at least two circuits are defective = 0.5+0.3+0.1 = 0.9

the probability that no more than two circuits are defective = probability that atleast two = 0.9

the mean in the probability distribution =

Standard deviation = 0.97976 = 0.98

Probability of no defects = 0.5

Each of the following is a requirement for a binomial distribution EXCEPT:

All outcomes must be classified into 2 or more categories

explanation : outcomes need not be more than 3 types or 3 categories

The probability that among 13 test subjects, at least five answer the question correctly,

p(X<=5)

n=13, p =0.2, q=0.8

p(X=0)+p(X=1)+p(X=2)....p(X=5)

= 13C0 p^0 * q^13 + 13C1 * p^1 * q^12 + 13C2 * p^2 * q^11+ ...

= 0.9696

Air liner

p = 0.8

q=0.2

n = 15

p(X=10)

= nCr * p^r * q^(n-r)

= 15C10 * 0.8^10 * 0.2^(15-10)

= 0.1031

the probability that at least 10 flights arrive on time.

= 0.1642

the probability that at least 5 flights arrive late

= the probability that less than 10 flights arrive on time

= p(X<10) = 0.061

the probability that 7 or fewer flight arrive late.

= proabability that more than 7 arrive on time

= 0.9956 =0.996

The amount of rain during the next thunderstorm

the above random variable is contionuos (since 3.2cm is possible)

Sample size is too less to be a binomial distribution

Also selected 5 menmbers may not represent 100 people

X P(X) 0 0.5 1 0.3 2 0.1 3 0.1