In a recent Pew poll, 10% of adults said that they consider themselves to be “gamers.”

Assume that 18 adults are randomly sampled.

a. Use the binomial probability distribution to compute the probability that exactly three of them consider themselves to be gamers.

b. Use Table A.1 to find the probability that fewer than two of them consider themselves to be gamers.

c. Use any valid method to find the probability that more than two of them consider themselves to be gamers.

d. Use any valid method to find the probability that the number who consider themselves to be gamers is between 1 and 4 inclusive.

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Table A.1 Binomial Probabilities P(x)= n! x!(n-x)!" p'(1-p)(-x) P nx 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.90 0.95 2 0 0.903 0.810 0.640 0.563 0.490 0.360 0.250 0.160 0.090 0.063 0.040 0.010 0.003 1 0.095 0.180 0.320 0.375 0.420 0.480 0.500 0.480 0.420 0.375 0.320 2 0.003 0.010 0.040 0.063 0.090 0.160 0.250 0.360 0.490 0.563 0.640 0.810 0.180 0.095 0.903 3 0123 0 0.857 0.729 0.512 0.422 0.343 0.216 0.125 0.064 0.027 0.016 0.135 0.243 0.384 0.422 0.441 0.432 0.375 0.288 0.189 0.007 0.027 0.096 0.141 0.189 0.288 0.375 0.432 0.441 0.422 0.000+ 0.001 0.008 0.016 0.027 0.064 0.125 0.216 0.343 0.422 0.512 0.008 0.141 0.096 0.027 0.007 0.384 0.243 0.135 0.729 0.857 0.001 0.000+ 4 01234 0.815 0.656 0.410 0.316 0.240 0.130 0.063 0.026 0.008 0.004 0.002 0.000+ 0.000+ 0.171 0.292 0.410 0.422 0.412 0.346 0.250 0.154 0.076 0.047 0.026 0.004 0.000+ 0.014 0.049 0.154 0.211 0.265 0.346 0.375 0.346 0.265 0.211 0.154 0.049 0.014 0.000+ 0.004 0.026 0.047 0.076 0.154 0.250 0.346 0.412 0.422 0.000+ 0.000+ 0.002 0.004 0.008 0.026 0.063 0.130 0.240 0.316 0.410 0.410 0.292 0.171 0.656 0.815 5 0 0.774 0.590 0.328 0.237 0.168 0.078 0.031 0.010 0.002 0.001 0.000+ 0.000+ 0.000+ 0.204 0.328 0.410 0.396 0.360 0.259 0.156 0.077 0.028 0.015 0.006 0.000+ 0.000+ 234 in 2 0.021 0.073 0.205 0.264 0.309 0.346 0.313 0.230 0.132 0.088 0.051 0.008 0.001 3 0.001 0.008 0.051 0.088 0.132 0.230 0.313 0.346 0.309 0.264 0.205 0.073 0.021 0.000+ 0.000+ 0.006 0.015 0.028 0.077 0.156 0.259 0.360 0.396 0.410 0.328 0.204 5 0.000+ 0.000+ 0.000+ 0.001 0.002 0.010 0.031 0.078 0.168 0.237 0.328 0.590 0.774