The number of companies is quite large. That is, n is quite large.
The probability that a company declares bankruptcy is quite small , p is quite small.
np = the mean number of bankruptcies = 2 = a finite number.
Hence we can apply Poisson distribution for the data.
P (x=5 | mean =2) = e-2 25/5! = e-2 * 32/120 = 0.036089
Alternatively
=poisson(5,2,0) = 0.036089
P(x≥ 5 | mean =2) = 1- P( x ≤ 4) = 1- e-2 (1+2+22/2!+23/3!+24/4!)= 1-e-2 (1+2+2+8/6+16/24)= 1-e-2(7)
=0.052653
Alternatively
= 1- poisson(4,2,1) =0.052653
P(X > 5 | mean =2) = 1- p(x
≤ 5) =1- e-2 (1+2+22/2!+23/3!+24/4!+25/5!)= 1-e-2(7+4/15)
=0.016564
alternatively=1-poisson(5,2,1)
=0.016564
X= 0.09629120 ..., —2.59629120...
Answer:
There are no pictures but the dialtion would be the same figure but in an increased size. If you add pictures I can give you a more definite answer
let's firstly convert the mixed fractions to improper fractions and then multiply.
![\bf \stackrel{mixed}{4\frac{3}{5}}\implies \cfrac{4\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{23}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{23}{5}\cdot \cfrac{2}{3}\implies \cfrac{23\cdot 2}{5\cdot 3}\implies \cfrac{46}{15}\implies 3\frac{1}{15}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B3%7D%7B5%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%205%2B3%7D%7B5%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B23%7D%7B5%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B23%7D%7B5%7D%5Ccdot%20%5Ccfrac%7B2%7D%7B3%7D%5Cimplies%20%5Ccfrac%7B23%5Ccdot%202%7D%7B5%5Ccdot%203%7D%5Cimplies%20%5Ccfrac%7B46%7D%7B15%7D%5Cimplies%203%5Cfrac%7B1%7D%7B15%7D)
