An airline reports that if 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.

Mean = np = 150 * .15 = ?

Standard deviation = √npq = √(150 * .15 * .85) = ?

Note: q = 1 - p

I'll let you finish the calculations.

Once you have the mean and standard deviation, use z-scores:
z = (x - mean)/sd
Note: x = 20

After you calculate z, check a z-table to find your probability. (Remember that the problem is asking for "fewer than 20" when you check the table.)

I hope this will help get you started.

To find the probability that there will be fewer than 20 no-shows, we can use the binomial distribution.

The binomial distribution is a probability distribution that gives the probability of obtaining exactly k successes in n independent Bernoulli trials, where each trial has a constant probability of success.

In this case, the probability of a no-show is 15%, or 0.15. The number of trials is 150, which represents the 150 advanced reservations. We want to find the probability of having fewer than 20 no-shows.

To calculate this probability, we can sum up the individual probabilities of having 0, 1, 2, ..., 19 no-shows using the binomial probability formula.

The binomial probability formula is:

P(x) = (nCx) * p^x * (1 - p)^(n - x)

Where:
P(x) is the probability of x successes,
nCx is the number of combinations of n items taken x at a time,
p is the probability of success in a single trial, and
n is the total number of trials.

In our case:
p = 0.15 (probability of a no-show),
n = 150 (number of advanced reservations), and
x = 0, 1, 2, ..., 19 (number of no-shows from 0 to 19).

We need to calculate the probabilities for each value of x and sum them up to get the final probability.

To simplify this process, we can use a statistical software or calculator, such as Excel, to calculate the probabilities for each value of x and then sum them. You can also use online binomial probability calculators, which allow you to input the values and get the result directly.

Using Excel, you can use the BINOM.DIST function to calculate the individual probabilities and then use the SUM function to sum them up.

For example, in Excel, you can use the following formula to calculate the probability of having exactly 0 no-shows:

=BINOM.DIST(0, 150, 0.15, FALSE)

Repeat this formula for x values from 0 to 19 and then sum up the results using the SUM function.

Finally, the resulting probability will be the sum of these individual probabilities.