80% of college freshmen admit to checking emails at least once per day. In a random sample of 10 freshmen: (Use 3 decimals for your answers)80% of college freshmen admit to checking emails at least once per day. In a random sample of 10 freshmen: (Use 3 decimals for your answers)

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:

$P(x=10)=(\genfrac{}{}{0ex}{}{n}{x})\cdot p^x\cdot (1–p{)}^{n–x}=(\genfrac{}{}{0ex}{}{10}{10})\cdot {0.8}^{10}\cdot (1–0.8{)}^{10–10}=0.1074\approx 0.107$

(B) The probability that at least 8 of them check their e-mail at least once per day:

$P(x\ge 8)=\sum _8^{10}(\genfrac{}{}{0ex}{}{n}{x})\cdot p^x\cdot (1–p{)}^{n–x}=\sum _8^{10}(\genfrac{}{}{0ex}{}{10}{x})\cdot {0.8}^x\cdot (1–0.8{)}^{10–x}=0.6778\approx 0.678$

(C) The probability that fewer than 7 check their e-mail at least once per day:

$P(x<7)=\sum _0^6(\genfrac{}{}{0ex}{}{n}{x})\cdot p^x\cdot (1–p{)}^{n–x}=\sum _0^6(\genfrac{}{}{0ex}{}{10}{x})\cdot {0.8}^x\cdot (1–0.8{)}^{10–x}=0.1209\approx 0.121$