Question

9. An express delivery service advertises next-day delivery of any parcel it receives before 3PM. The actual success rate is 90%. A random sample of 16 parcels were chosen.

a. Calculate the probability that all 16 were delivered by the next day.


b. What is the probability that 12 or fewer were delivered on time?

Answer 1

a) P(X =16 ) = 0.1853

b)
`P(X \leq 12)` = 0.0684

Explanation:

GIVEN DATA:

n = 16

p = 0.90

from relation given probabllity can be solve

`P(X) = ^nC_x * p^x * ( 1 - p)^(n-x)`

a)

`P(X =16 ) = ^(16)C_(16) * 0.90^x * ( 1 - 0.90)^(16-16)`

P(X =16 ) = 0.1853

b)
`P(X \leq 12) = 1 - P(X \geq 13)`

= 1 - [ P(X = 13) +P(X = 14) +P(X = 15) +P(X = 16) ]

`= 1 - [ ^(16)C_(13) * 0.90^(13) * (1 - 0.90)^3 +^(16)C_(14) * 0.90^(14) * (1 - 0.90)^2 +^(16)C_(15) * 0.90^(15) * (1 - 0.90)^1 +^(16)C_(16) * 0.90^(16) * (1 - 0.90)^0 ]`

= 0.0684