Question

Assume that when adults with smartphones are randomly​ selected, 5​% use them in meetings or classes. If 7 adult smartphone users are randomly selected, find the probability that at least 5 of them use their smartphones in meetings or classes.

The probability is ____.

Answer 1

We are given that 5% of the randomly selected adults with smartphones use them in meetings or classes. It means that when an adult with smartphone is randomly selected the probability that he/she uses it in meetings or classes is 5% = 0.05.

Let X denote the number of adult smartphone users (out of the 7 randomly selected) who use them in meetings or classes.

Since, there is a fixed number of adults with smartphones in the sample (fixed number of trials), each adult with smartphone has two outcomes (using or not using it in meetings or classes) and each adult with smartphone uses it in meetings or classes with probability 0.05 independent of other adults with smartphones. Thus, we can conclude that:
X ~ Binomial(n=7, p=0.05)

Thus, the probability mass function of X is given by:

Thus, the probability that at least 5 (of the 7 randomly selected adults with smartphones) use them in meetings or classes is given by:

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