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MakcuM [25]
3 years ago
8

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list sh

e doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number on non-authentic names in her sample, the expected (average) value of x is ______________.
a) 2.50
b) 2.00
c) 1.50
d) 1.25
e) 1.35
Mathematics
1 answer:
DaniilM [7]3 years ago
8 0

Answer:

b) 2.00

Step-by-step explanation:

For each name, there are only two possible outcomes. Either it is authentic, or it is not. The probability of a name being authentic is independent of any other name. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

E(X) = np

She randomly selects five names from the list for validation.

This means that n = 5

40% of the names on the list are non-authentic

This means that p = 0.4

The expected (average) value of x is

E(X) = np = 5*0.4 = 2

The correct answer is given by option B.

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