Question

Help me with this math problem

Answer 1

The required probabilities are as follows:

a) P(X=5) = 0.123

b) P(X6) = P(X=6+X=7+X=8+X=9+X=10)

c) P(X4)=P(X=0), P(X=1), P(X=2), and P(X=3)

Using a binomial random variable, the following is modeled:

There are always ten (10) persons that are being questioned.

From trial to trial, the likelihood of success (i.e., very little faith in newspapers) remains consistent (p=0.68).

The trials are impartial (a reasonable assumption, since the response of 1 of the people should not affect the response of any other)

There are just two possible results for each trial: low faith in newspapers or not.

X counts how many of the 10 trials were successful.

P(X=k) = is the probability mass function for the binomial random variable.

= $^nC_k\times(p^k)\times(1-p)^{n-k}$

a) P(X=5) =$^{10}C_5\times(0.68)^5\times(0.32)^5$≈ 0.123

b) P(X6) = P(X=6+X=7+X=8+X=9+X=10)

These may all be calculated individually, then summed together.

c) P(X4)=P(X=0), P(X=1), P(X=2), and P(X=3)

the same concept as in (b) above.

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