SECTION 4.2 Binomial Distributions 205 Finding Binomial Probabilities In Examples 2 and 3, you used the binomial probability formula to find the probabilities. A more efficient way to find binomial probabilities is to use technology. For instance, you can find binomial probabilities using Minitab, Excel, StatCrunch, and the TI-84 Plus. Finding a Binomial Probability Using Technology A survey found that 75% of U.S. adults are experiencing digital device fatigue. (This is the state of mental exhaustion caused by concurrent and excessive use of digital devices such as smartphones and tablet computers.) You randomly select 100 adults. What is the probability that exactly 66 are experiencing digital device fatigue? Use technology to find the probability. (Source: The Harris Poll) SOLUTION Minitab, Excel, StatCrunch, and the TI-84 Plus each have features that allow you to find binomial probabilities. Use such technologies to obtain results similar to these displays. STATCRUNCH Binomial Calculator n:100 p:0.75 P(X = 66) = 0.01116782 MINITAB Probability Density Function Binomial with n = 100 and p = 0.75 x P(X = x) 66 0.0111678 TI-84 PLUS binompdf(100, .75, 66) .0111678235 EXCEL 0.011167823 A =BINOM.DIST(66,100,0.75,FALSE) 1 Interpretation From these displays, you can see that the probability that exactly 66 adults are experiencing digital device fatigue is about 0.011. Because 0.011 is less than 0.05, this can be considered an unusual event. TRY IT YOURSELF 4 A survey found that 28% of U.S. employees will work from home full-time over the next few months. You randomly select 150 adults. What is the probability that exactly 30 will work from home full-time over the next few months? Use technology to find the probability. (Source: The Harris Poll) Answer: Page A38 EXAMPLE 4 Tech Tip You can use technology such as Minitab, Excel, StatCrunch, or the TI-84 Plus to find a binomial probability. For instance, here are instructions for finding a binomial probability on a TI-84 Plus. From the DISTR menu, choose the binompdf( feature. Enter the values of n, p, and x. Then calculate the probability. Study Tip Recall that a probability of 0.05 or less is considered unusual.
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