Intergalactic president Zaphod Beeblebrox enjoys a 78% approval rating among residents of planets in the vicinity of Betelgeuse.

Question

Find the probability that at most 109 residents of planets near Betelgeuse, taken out of a random sample of 126, approve of Zaphod Beeblebrox.

Answer 1

You can also do this with Excel.

For the PC version of Excel, go to any open cell and start typing

=Binom

Double-click the Binom.Dist function from the pop-up window. Next, you need to type four numbers, each separated by a comma:

Number of successes,

Number of trials,

Probability of success,

Cumulative? A "1" here means to add up all the probabilities up to this point; a "0" means just give me the P(x) for that value of "x."

So your full formula looks like

=Binom.Dist(109, 126, 0.78, 1)

Hit enter. The answer is 0.994407 (to six decimal places).

Answer 2

Hi Madison,

This is a binomial probability distribution, but the values are far too high to compute by hand. Formula is typically:

P(X=x) = C(n,x)*p^x*q^n-x

n = sample size = 126

x = number of successes = 108

p = probability of success = 0.78

Furthermore, we want probability of 109 residents AT MOST, which means we would have to compute everything from 0 to 109 or from 110 to 126 and use complement rule. It is not practical, so we turn to technology. The TI-80s series graphing calculators have a function for this. Go to:

2nd-VARS-binomcdf (n,p,x)

This function is specifically designed to compute probability of x successes at most—sums all values to that mark. Anyhow,

2nd-VARS-binomcdf(126, 0.78, 109) = 0.994

I hope this helps.