Question

In learning how to fold a paper rose, only 30% of people will be able to successfully fold a paper rose on their first try.
a) A random sample of 20 individuals were selected and instructed how to fold a paper rose. What is the probability that no more than 45% of them are successful on their first try?
b) Suppose you repeat your experiment in (a) six times, and each time at least 45% of individuals are successful on their first try. How likely is this to occur? What conclusions can you draw on the quoted success rate? Give a logical explanation and
support your response with any appropriate numerical evidence.

Answer 1

a.

P(x people successful) = 20Cx * (0.3^x) * (1-0.3)^(20-x)

P(p<=0.45) = P(x<=0.45*20)

= P(x<=9)

= P(0)+P(1)+....+P(9)

= 0.9520

probability that no more than 45% of them are successful on their first try = 0.9520

b.

P(p>=0.45) = 1 -0.9520 = 0.0480

P(p>=0.45 all 6 times) = (0.0480)^6 = 1.2231*10^(-8)

P(p>=0.45 all 6 times) = 1.2231*10^(-8)

from the success rate we cann say on average 30% people will be able to fold on first try

since each participant's success is independent it is binomial distribution

so : expected no. of success = n*p = 20*0.3 = 6

so, on average 6 people will successfully fold rose on first try

( please UPVOTE)