To calculate binomial probabilities in EXCEL, we use the builtin BINOMDIST function:

Let n = # trials, p = probability ofsuccess on a single trial

==> Prob of exactly k successes = P(X =k) = BINOM.DIST(k, n, p, FALSE)

==> Prob of at most k successes = P(X

Note that these can be used in conjunction with the basic rules ofprobability to calculate other probabilities.

For example, the probability of at leastk successes is P(X > k) = 1 – P(X <k – 1).
In particular, the probability of at least one success is P(X >1) = 1 – P(X = 0).

* * * *

To calculate normal probabilities in EXCEL, we use the built inNORMDIST function:
If we have a normal distribution with mean m and standard deviations, then

==> P( X < k) = NORM.DIST(k, m, s,TRUE)

I.e. NORMDIST gives the CUMULATIVE probability

Again, this can be used in conjunction with basic rules ofprobability to compute other probabilities. Forexample:

=> P( X > k) = 1 – P(X < k) = 1 – NORMDIST(k, m,s, TRUE)

=> P(a < X <b) = NORMDIST(b, m, s, TRUE)– NORMDIST(a, m, s, TRUE)

Occasionally, we have a probability, and need to find thecorresponding data value.
This can also be done with EXCEL:

Go to INSERT >> FUNCTION >> STATISTICAL >>NORMINV

è NORMINV( p , m, s) returns the value k so that p = P( X < k).

Solve each of the following problems using the built-infunctions in Excel.

For each problem, identify the type of distribution (binomial ornormal), and clearly write the probability beingcalculated: E.g. P(X > 3), P(X <5.2), etc.
Use the Excel commands from the previous page to do thecalculations.
Save your work to an Excel file and submit via theAssignment Link in Blackboard.


1. A car insurance company has determined that 8% ofall drivers were involved in a car accident last year. If 15drivers are randomly selected, what is the probability of getting 3or more who were involved in a car accident last year?

2. On a certain daily flight, Air Northeast has a policyof booking as many as 22 people on an airplane that can seat only19. Past studies have revealed that only 89% of the bookedpassengers actually arrive for the flight. If theairline books 22 people on a flight, find the probability thatthere will not be enough seats available for all bookedpassengers. Show sufficient work to justify answer.

3. A manufacturing company measures the weight of boxesbefore shipping them to the customers. Assume that theweights of boxes are normally distributed with mean 90 lbs andstandard deviation 24 lbs.

a) Find the probability that arandomly selected box will exceed 94 lbs.

b) If a sample of 36 boxes israndomly selected, find the probability that theaverage
of the boxesexceeds 94 lbs.

4. An employer wants to estimate to set a time limit sothat 90% of the employees will finish a job on time. Past historyhas shown that the time required to do the job is normallydistributed and has a mean time of 32 minutes with a standarddeviation of 6 minutes. How much time should the employer allowemployees to finish the job?
(Round to the nearest minute.)