in a large survey, it was discovered that 1 out of every 5 adults visits disney world every year. if 30 adults are randomly selected, what is the probability that exactly 7 of them will visit disney world this year.

prob of visit = 1/5 = p = .2

Binomial dist:
p(x = 7) = [30:7] .2^7 (.8)^23
look up binomial coef [30:7]
or use formula
30!/[7!(23!)]

30!/23!/7! = 30*29*28*27*26*25*24/(7*6*5*4*3*2)
= 29*28*27*26*25*24/(7*6*4)
= 29*4*26*25 = 75,400

then
p = 75,400 (.2^7)(.8^23)
= .005697

prob to go Disney = 1/5

prob not to go Disney = 4/5

prob that 7 of 30 will go
= C(30,7)(1/5)^7 (4/5)^23 = appr. .1538

binomial coef error

coef = 2035800 not 75,400
30!/23!/7! = 30*29*28*27*26*25*24/(7*6*5*4*3*2)
2035800

p = 2035800 (.2^7)(.8^23)
= .1538

To calculate the probability that exactly 7 out of 30 adults will visit Disney World this year, we can use the binomial probability formula. The probability of success (visiting Disney World) for each trial is 1/5 since 1 out of 5 adults visit. Let's break down the steps to get the answer:

Step 1: Determine the number of trials, n.
In this case, the number of trials is 30 because we are randomly selecting 30 adults.

Step 2: Determine the probability of success, p.
The probability of success (visiting Disney World) is 1/5 or 0.2.

Step 3: Determine the desired number of successes, x.
We want exactly 7 adults to visit Disney World.

Step 4: Calculate the binomial probability using the formula:
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))
where (nCx) represents the number of combinations of n items taken x at a time.

Using the values from steps 1-3:
n = 30, p = 0.2, x = 7

P(7) = (30C7) * (0.2^7) * ((1-0.2)^(30-7))

Step 5: Calculate the combinations using the formula:
(nCx) = n! / (x! * (n-x)!)
where n! represents the factorial of n.

Calculating (30C7):
(30C7) = 30! / (7! * (30-7)!)
(30C7) = (30!)/(7! * 23!)

Using this formula, you can calculate P(7) using a calculator or a statistical software.

Alternatively, you can use online calculators or statistical software specifically designed for binomial probability calculations, making it easier and faster to find the answer.