Tony’s Pizza Company finds that 65% of the general population likes pepperoni pi
ID: 3181607 • Letter: T
Question
Tony’s Pizza Company finds that 65% of the general population likes pepperoni pizza. I buy pizza for 56 of my intro stats students and it turns out that only 30 of these students like pepperoni pizza. (a) Using the normal approximation to the binomial distribution, what is the probability of getting 30 or fewer students who like pepperoni pizza in a randomly selected group of 56 students? Tony’s Pizza Company finds that 65% of the general population likes pepperoni pizza. I buy pizza for 56 of my intro stats students and it turns out that only 30 of these students like pepperoni pizza. (a) Using the normal approximation to the binomial distribution, what is the probability of getting 30 or fewer students who like pepperoni pizza in a randomly selected group of 56 students? Tony’s Pizza Company finds that 65% of the general population likes pepperoni pizza. I buy pizza for 56 of my intro stats students and it turns out that only 30 of these students like pepperoni pizza. (a) Using the normal approximation to the binomial distribution, what is the probability of getting 30 or fewer students who like pepperoni pizza in a randomly selected group of 56 students?Explanation / Answer
Let X denote the number of students who like pepperoni pizza , the as sample size n=56>30, we use normal approximate that X follows normal distribution with man=np=56*0.65 =36.4 and standard deviation =sqrt(n*p*(1-p))
=sqrt(56*0.65*(1-0.65)) =3.57
so, the probability of getting 30 or fewer students who like pepperoni pizza in a randomly selected group of 56 students=P(X<=30)
=P(X<30+0.5) using continuty correction
=P(X<30.5)
=0.0492 using excel fucntion =NORMDIST(30.5,36.4,3.57,TRUE)