Example 18

EXAMPLE 18Using technology to find binomial probabilities

Using the binomial distribution from Example 16, use the TI-83/84 and CrunchIt! to find the following probabilities:

$P (X = 4)$ , the probability that all four Americans are sleep-deprived.
$P (X \leq 2)$ , the (cumulative) probability that, at most, two Americans are sleep-deprived.

Solution

Figure 9 shows that we use the TI-83/84 function binompdf with $n = 4$ , $p = 0.2$ , and $X = 4$ . Figure 10 shows the result: $P (X = 4) = 0.0016$ . Figure 11 shows the same input and final answer using CrunchIt!.

FIGURE 9 TI-83/84 menu.

FIGURE 10 TI-83/84 result.

FIGURE 11 CrunchIt!
With the TI-83/84, we use the function binomcdf with $n = 4$ , $p = 0.2$ , and $X = 2$ . Figure 12 shows the result: $P (X \leq 2) = 0.9728$ . Figure 13 shows the input and final answer using CrunchIt!.

FIGURE 12 TI-83/84 result.

FIGURE 13 CrunchIt!

NOW YOU CAN DO

Exercises 29–48.