Question

Assume that when adults with smartphones are randomly​ selected, 61% use them in meetings or classes. If 8 adult smartphone users are randomly​ selected, find the probability that exactly 3 of them use their smartphones in meetings or classes

Answer 1

Answer:

0.1147

Step-by-step explanation:

When adults with smartphones are randomly​ selected, 61% use them in meetings or classes, then

• the probability of using the smartphone is $p=0.61;$

• the probability of not using the smartphone is $q=1-p=1-0.61=0.39.$

If 8 adult smartphone users are randomly​ selected, the probability that exactly 3 of them use their smartphones in meetings or classes can be calculated using binomial distribution as

$C^8_3\cdot p^3\cdot q^{8-3}=C^8_3\cdot (0.61)^3\cdot (0.39)^5$

Note that

$C^8_3=\dfrac{8!}{3!(8-3)!}=\dfrac{5!\cdot 6\cdot 7\cdot 8}{2\cdot 3\cdot 5!}=\dfrac{6\cdot 7\cdot 8}{2\cdot 3}=7\cdot 8=56,$

then the probabilty is

$56\cdot (0.61)^3\cdot (0.39)^5\approx 0.1147$