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question 2: a federal report finds that a lie detector test given to truthful persons
have a probability of 0.2 of suggesting that the person is deceptive. a company
asks 12 job applicants to take a lie detect test. suppose that all 12 applicants
answer truthfully.
. what is the probability that exactly one is being deceptive?
. what is the probability that at most one is being deceptive?
• what is the mean and standard deviation of this distribution?
i need with the last two questions.
what is the probability that at most one is being deceptive?
what is the mean and standard deviation of this distribution?

P(Exactly 1 is being deceptive) is 0.2062 .

P(At most 1 is being deceptive) is

Mean of the distribution is, 2.4 and standard deviation of the distribution is,

Step-by-step explanation:

Let, the no. of truthful persons suggested as deceptive by the lie-detector test be denoted by the random variable X. Then, according to the question, in this case,

X Binomial (12, 0.2)

So, here,

1. No. of trials = 12 = n (say)

2. Probability of success = 0.2 = p (say)

3. Probability of failure = (1 - 0.2) = 0.8 = q (say)

So,

P(Exactly 1 is being deceptive)

= P(X = 1)

=

0.2062 ---------------(1)

P(At most 1 is being deceptive)

= P(X = 0) + P(X = 1)

=

                         [From (1)  putting the value of P(X = 1)]

= 0.2749

Mean of the distribution =

                                        =

                                         = 2.4

Standard deviation of the distribution,

                                       =

                                       =

o

Step-by-step explanation:

Recognize, describe, and calculate the measures of the center of data: mean, median, and mode. The “center” of a data set is also a way of describing location.