SOLUTION: I really don't understand how to do this. I'm sure there is a way to do this on a scientific calculator, but for the life of me, I can't figure it out! Thanks so much for your

Question 380949: I really don't understand how to do this. I'm sure there is a way to do this on a scientific calculator, but for the life of me, I can't figure it out!
Thanks so much for your help!
A local concert center reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, find the probability that there will be fewer than 20 no-shows.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A local concert center reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, find the probability that there will be fewer than 20 no-shows.

15% * 150 = 22.5

This looks like a normal distribution type of problem.

The probability that there will be fewer than 20 no-shows is equal to the probability that there are 0 no-shows plus 1 no-show plus 2 no-show + ... 19 no-shows.

I scoured the web for an answer because this problem appears to be too difficult to manually calculate.

I figured there must be a formula or calculator that allows you to calculate this.

What I found was on stattrek.com

It's called a binomial distribution calculator.

It's used to calculate probabilities where the outcome is either success or failure.

success in your problem would be a no-show.

you would go to the following web address:

http://stattrek.com/Tables/Binomial.aspx#experiment

You would enter the probability of success as being .15
You would enter the number of trials as 150.
You would enter the number of successes as 20.
The calculator does the rest.

The calculator gives you all the pertinent statistics.
In this case, the statistic you are looking for would be p(x<20) = .250928195415981 which you can round to whatever decimal place you require.

It's hard to manually calculate with 150 trials, but if the number of trials were something smaller, like 3, then it would be easier to manually calculate the probability of getting less than 2 no shows.
the calculator would give you the answer of:
p(x<2) = .93925

You would manually calculate it as follows:

p(x=0) = .85*.85*.85 = .614125 * 1 = .614125
p(x=1) = .15*.85*.85 = .108375 * 3 = .325125
p(x=2) = .15*.15*.85 = .019125 * 3 = .057375
p(x=3) = .15*.15*.15 = .003375 * 1 = .003375

If you did it correctly, then the total probability should equal 1 which it does.

If you did it correctly, then the p(x<2) = .614125 + .325125 = .93925 which agrees with what the calculator did for you.

The multipliers are required based on the combination formula of n! / (x! * (n-x)!)

for x = 1, you get n = 3 and x = 1 to get 3!/(1!*2!) = 3

for x = 2, you get n = 3 and x = 2 to get 3! / (2!*1!) = 3

for x = 0, you get n = 3 and x = 0 to get 3! / (0!*3!) = 3!/3! = 1

for x = 3, you get n = 3 and x = 3 to get 3! / (3!*0!) = 3!/3! = 1

The binomial calculator does all the work for you.

There may be a formula to allow you to do it manually, but I don't know it.

I think the calculator just crunches the numbers, but I won't swear to that.

Try it out and see how it works for you.

It's easy to calculate each probability.

Just change the number of successes and crunch the numbers again using the calculator.

Make sure you hit the calculate button.

Just hitting the return doesn't recalculate.

It might look like it does, but it doesn't.

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