SOLUTION: 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

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Question 1136954: 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?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
p = .65
q = 1 - p = .35
n = 56
x = 30

in the binomial distribution, mean of the sample = n * p = .65 * 56 = 36.4

standard deviation of the distribution of sample means is equal to sqrt( n * p * q) = sqrt( 56 * .65 * .34) = sqrt(12.74) = 3.56931366.

using the online normal distribution calculator found at , you would find that the probability of 30 or fewer of the students out of 56 students liking pepperoni pizza is equal to .0492.

i used excel to determine what the actual probability would be.

in excel, i used the binomial probability formula of p(x) = p^x * q^(n-x) * c(n,x).

n is equal to 56.
p is equal to .65
q is equal to .35
x is equal to the number of people who like pepperoni pizza.

excel told me that the probability of 30 or fewer liking pepperoni pizza was .051113.

there is an online calculator that tells you what the binomial probability would be and also what the normal approximation to the binomial probability would be.

that calculator can be found at https://homepage.divms.uiowa.edu/~mbognar/applets/binnormal.html

it confirmed that the normal approximation to the binomial probability is .0492 and the binomial probaiblity is .051113 as i had determined from the use of excel.

here's a display of use of the normal distribution calculator.

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here's a display of use of the binomial probability and normal approximation calculator.

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here's a display of the use of excel.

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the excel is the most detailed because it shows the probability of every x from 0 to 56.