10 According to the Deloitte EV Survey 5 of respondents indi

10. According to the Deloitte EV Survey, 5% of respondents indicated that they would be willing to pay an extra $500 or more for an electric vehicle versus one with a gasoline engine. A random sample of 25 adults has been selected. Use the Poisson distribution to approximate the binomial distribution to determine the probability that three or four adults from this sample would be willing to pay an extra $500 or more for an electric vehicle versus one with a gasoline engine.

Solution

n = 25, p = 5% = 0.05

Hence mean = np = 1.25

POisson distribution approximated has a parmaeter equal to 1.25

P(X=3 or 4) = P(X=3) +P(x=4) =0.0933+0.0291

= 0.1224