This set of Statistical Quality Control test focuses on “Continuous Distributions – 2”.

1. The display of possible outcomes of an event with their corresponding probabilities is called ____

a) Probability Plot

b) Contingency table

c) Bayesian Table

d) Frequency Plot

View Answer

Explanation: The graphical representation of possible outcomes of an event with their corresponding probabilities; is called Probability plot.

2. Which one of these is not one of the conditions for the binomial distribution?

a) Only two outcomes must be there for an event

b) Independent trials must be there

c) Trials must be more than 4

d) The probability of failure must be constant

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Explanation: For a binomial distribution, Bernoulli trials are necessary, i.e. the outcomes of an event must be either a success or a failure, and this means the probability of failure must be constant.

3. For mean=7 and standard deviation=2, what will be probability that a variable, which follows normal distribution, will have a value less than or equal to 10?

a) 0.93319

b) 0.94520

c) 0.96409

d) 0.91924

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4. The variance of lognormal distribution is given by ____

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Explanation: The variance of a variable having a lognormal distribution is given by,

σ

^{2}= e

^{2θ+w2}(e

^{w2}-1).

5. The relationship between the mean and variance of the exponential distribution is expressed by _____

a) μ= λσ^{2}

b) μ= σ^{2}/λ

c) σ^{2}=λ^{2} μ

d) σ^{2}=μ/λ^{2}

View Answer

Explanation: For an exponential distribution, μ=

^{1}⁄

_{λ}and σ

^{2}= 1/λ

^{2}

So, for an exponential distribution, μ= λσ

^{2}.

6. (1-e^{-λa}) is the cumulative ______ distribution.

a) Gamma

b) Normal

c) Lognormal

d) Exponential

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Explanation: The cumulative distribution for standard exponential distribution is given by following equation,

F(a)=(1-e

^{-λa}).

7. The exponential distribution is used in reliability engineering as a model of the time to failure of a system. The parameter λ is called _____ in this application.

a) Failure rate

b) MTF

c) Hazard rate

d) MTBF

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Explanation: The parameter λ in the reliability engineering application of the exponential distribution is called the failure rate of the system. The application uses it as a model of time to failure.

8. The mean of the exponential distribution used in the reliability engineering is used as mean time to failure.

a) True

b) False

View Answer

Explanation: In reliability engineering, the exponential distribution is used as a model of the time to failure of a system. The mean of the distribution is called MTF or mean time to failure.

9. The mean of the gamma distribution is given by ____

a) μ=1/λ

b) μ=r/λ

c) μ=r^{2}/λ

d) μ=1/r

View Answer

Explanation: For a gamma distribution,

μ=r/λ

Where r and λ are the shape parameter and the scale parameter, respectively.

10. Exponential distribution is a special case of gamma distribution.

a) True

b) False

View Answer

Explanation: When the shape factor r=1, in the case of a gamma distribution, gamma distribution reduces to an exponential distribution which has only the scale parameter λ.

11. The relationship between the mean and the standard deviation of the gamma distribution is given as _____

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12. If the shape parameter of the gamma distribution is twice the scale parameter, what will be the value of the mean of the distribution?

a) 1.5

b) 2

c) 4

d) 1

View Answer

Explanation: As for a gamma distribution, mean μ=r/λ; putting the value r=2λ from the question, we get,

μ=

^{2λ}⁄

_{λ}=2.

13. For an exponential distribution, what is the probability that the value of the exponential random variable with parameter λ=3.2; will be having a value higher than 0.2353?

a) 0.5290

b) 0.4710

c) 0.2213

d) 0.3452

View Answer

Explanation: P[x>0.2352]=1-P[x≤0.2352]=1-{1-exp(-3.2*0.2353) }=0.4710.

14. Which of these will not be distributed on a discrete distribution?

a) The number of houses in a colony

b) The number of bedrooms in a house

c) The number of scratches on a car hood

d) The diameter of a car tire

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Explanation: The number of houses, bedrooms, and scratches, are all incremented by a discrete number, which is an integer, whereas, the diameter of a car tire will be increased on a continuous scale. Thus, it must be plotted on a continuous distribution.

15. For a variable distributed log-normally with θ=6,ω=1.2; what is the probability that the variable exceeds a value of 500?

a) 0.4290

b) 0.5710

c) 0.4990

d) 0.4937

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**Sanfoundry Global Education & Learning Series – Statistical Quality Control.**

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