Homework SourseData collected by a major cell phone provider indicate that
Data collected by a major cell phone provider indicate that only 20% of cell phone customers are willing to switch cell phone providers. If a binomial process is assumed, then in a sample of 20 cell phone customers find the following:
- What is the probability that between 5 and 9 (including 5 and 9) will be switching their cell provider?
Data collected by a major cell phone provider indicate that only 20% of cell phone customers are willing to switch cell phone providers. If a binomial process is assumed, then in a sample of 20 cell phone customers find the following:
- What is the probability that between 5 and 9 (including 5 and 9) will be switching their cell provider?
- What is the probability that between 5 and 9 (including 5 and 9) will be switching their cell provider?
Solution
Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
P( X = 5 ) = ( 20 5 ) * ( 0.2^5) * ( 1 - 0.2 )^15
= 0.1746
P( X = 6 ) = ( 20 6 ) * ( 0.2^6) * ( 1 - 0.2 )^14
= 0.1091
P( X = 7 ) = ( 20 7 ) * ( 0.2^7) * ( 1 - 0.2 )^13
= 0.0545
P( X = 8 ) = ( 20 8 ) * ( 0.2^8) * ( 1 - 0.2 )^12
= 0.0222
P( X = 9 ) = ( 20 9 ) * ( 0.2^9) * ( 1 - 0.2 )^11
= 0.0074
P( 5 < X = 9) = 0.1746 + 0.1091 + 0.0545 + 0.0222 + 0.0074 = 0.3678
