In: Statistics and Probability
Probability of playing video games = p = 0.15 (15%=0.15)
Random Sample Size = n = 450
We will use Normal approximation to Binomial distribution in this case as sample size is quite large.
Let X denotes number of adults who play video games in the sample.
Mean = np = 450*0.15 = 67.5
Standard Deviation = = 7.575
We have to find the probability that fewer than 54 out of a random sample of 450 adults will play video games
i.e.
We get the phi value from Normal z table(attached).
The probability that fewer than 54 out of a random sample of 450 adults will play video games is 0.037
z table :