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Question

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7. A word is randomly selected from a newspaper article. A random variable X is defined as the number of letters in that word. What are the possible values of X?

X= {2, 3, ...}

X= {0, 1, 2, ...}

X= {1, 2, 3, ...}

X= {1, 2, 3, 4, 5}

8. A contestant receives $12 if a coin turns up heads and $4 if it turns up tails. What is the expected value of a trial?

$81

$80

$18

$8

9. Which of the following statement(s) is(are) a characteristic(s) of a binomial experiment?

The experiment consists of 'n' identical trials.

Each trial results in one of two outcomes, 'success' or 'failure'.

The probability of success on a single trial is equal to 'p' and remains the same from trial to trial. The probability of failure is equal to q = (1 - p).

The trials are independent.

We are interested in 'x', the number of successes observed during the 'n' trials, for x = 0, 1, 2, ..., n.

All of the above are characteristics of a binomial experiment.

Only some of the above are characteristics of a binomial experiment.

None of the above are characteristics of a binomial experiment.

10. From past experience, it is known that 90% of one-year-old children can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 20 one-year-old children are given this voice recognition test. Calculate the mean

1

2

18

19

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Explanation / Answer

7:

A word can have minimum one letter (like word a, I etc) and can have maximum any number of letters so X can take values 1, 2, 3,...

Answer: X= {1, 2, 3, ...}

8:

Probability of getting head: P(head) = 0.5

Probability of getting tail: P(tail) = 0.5

So requried expected value is

0.5 * 12 + 0.5 *4 = 8

Answer: $8

9:

All of the above are characteristics of a binomial experiment.

10:

Using binomial experiment we have p=0.90 and n =20

So requried mean is

mean = np = 20*0.9 = 18

Answer : 18

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Note:

Image of question 6 did not display so not possible to answer that question.

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