Answer:
Given Data :
Probability of success $(p)=0.8$
Sample size $(n) = 10$
(A) The probability that all of them admit to checking emails at least once per day:
$P(x = 10) = \binom{n}{x} \cdot p^x \cdot (1 – p)^{n – x} = \binom{10}{10} \cdot 0.8^{10} \cdot (1 – 0.8)^{10 – 10} = 0.1074 \approx 0.107$
(B) The probability that at least 8 of them check their e-mail at least once per day:
$P(x \geq 8) = \sum_{8}^{10} \binom{n}{x} \cdot p^x \cdot (1 – p)^{n – x} = \sum_{8}^{10} \binom{10}{x} \cdot 0.8^x \cdot (1 – 0.8)^{10 – x} = 0.6778 \approx 0.678$
(C) The probability that fewer than 7 check their e-mail at least once per day:
$P(x < 7) = \sum_{0}^{6} \binom{n}{x} \cdot p^x \cdot (1 – p)^{n – x} = \sum_{0}^{6} \binom{10}{x} \cdot 0.8^x \cdot (1 – 0.8)^{10 – x} = 0.1209 \approx 0.121$
