Question

According to TECH.CO, there are seven most common smartphone issues and there are simple fixes for most of them. One of the problems are phone crashes which accounted for approximately 25% of the performance issues.† Suppose that smartphones are shipped in lots of

N = 60

phones. Before shipment,

n = 9

phones are selected from a lot of

N = 60

phones that contains

M = 14

phones that will crash when tested. If there are no crashes among the 9 tested phones, the lot is shipped. If one or more crashes are observed, all 60 phones are tested.

(a)

What is the probability distribution for x, the number of phones that crash in the sample of

n = 9?

p(x) =

C

14

x

C

46

9 − x

C

60

9

for x = 0, 1, ..., 9p(x) =

C

60

9

C

14

x

C

46

9 − x

for x = 0, 1, ..., 9    p(x) =

C

60

9

C

14

x

C

46

9 − x

for x = 0, 1, ..., 9p(x) =

C

46

x

C

14

9 − x

C

60

9

for x = 0, 1, ..., 9p(x) =

C

60

9

C

46

x

C

14

9 − x

for x = 0, 1, ..., 9

(b)

What is the probability that the lot is shipped? (Round your answer to three decimal places.)

(c)

What is the probability that all 60 phones will be tested? (Round your answer to three decimal places.)

Answer 1

it is hypergeometric distribution          
and probability is given by           
P(X=x) =C(k,x)*C(N-k,n-x)/C(N,n)          

where      
Sample size,     n =    9
No. of events of interest in population    , k =   14
Population size   , N =   60

a)

P(X) = C(14,x) C(46,9-x) / C(60,9)

b) P(lot is shipped) = P(X=0)= C(14,0)*C (46,9)/C(60,9)           =   0.075

c) P(all 60 phones will be tested) = 1 - P(X=0) = 1-0.0745 = 0.925