Suppose approximately 80% of all marketing personnel are extroverts, whereas about 55% of all computer programmers are introverts. (Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?

The probability that 10 or more are extroverts is

Step-by-step explanation:

We are given that approximately 80% of all marketing personnel are extroverts, whereas about 55% of all computer programmers are introverts.

Also, a sample of 15 marketing personnel is chosen.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 15 marketing personnel

             r = number of success = 10 or more

            p = probability of success which in our question is % of marketing

                  personnel that are extroverts, i.e; 80%

LET X = Number of marketing personnel that are extroverts

So, it means X ~

Now, Probability that 10 or more are extroverts is given by = P(X 10)

P(X 10)  = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

=

=

= 0.1032 + 0.1876 + 0.2501 + 0.2309 + 0.1319 + 0.0352 = 0.9389

So, the probability that 10 or more are extroverts is 0.9389.