Question

At a certain fast food restaurant, 77.5% of the customers order items from the value menu. If 14 customers are randomly selected, what is the probability that at least 9 customers ordered an item from the value menu? Use Excel to find the probability.

Answer 1

Let the number of customers who ordered an item from the value menu be denoted by X. Thus; X ~ binomial (14, 0.775)

Required probability = P(X 9) = 1 - P(X8) = 1 - F_X(8) where F_X(x) is the CDF of X at x.

Calculating binomial probability in Excel is done as follows :-

SYNTAX :-

BINOM.DIST(number_s,trials,probability_s,cumulative)

The BINOM.DIST function syntax has the following arguments:

• Number_s     Required. The number of successes in trials.

• Trials     Required. The number of independent trials.

• Probability_s     Required. The probability of success on each trial.

• Cumulative     Required. A logical value that determines the form of the function. If cumulative is TRUE, then BINOM.DIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.

So choose a random cell and write the function :- = 1 - BINOM.DIST(8,14,0.775,TRUE)

Using this function, we get the required probability = 0.927234317