Question

      9. Quality improvement in medical billing has been greatly improved. It is reported that only

            4% (.04) of medical records have had a mistake that had to be corrected. If thirty (30)

            records were selected at random, what is the probability that:

                           a. None of these records contained an error?

                           b. Exactly five (5) records contained an error?

                           c. No more than two (2) records contained an error?

                            d. Less than four (4) records contained an error?

                            e. At least one (1) record contained an error?

                            f. Greater than three (3) records contained an error?

                            g. Exactly one (1) record contains an error?

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other.

Here we need to use the binomial formula.

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.04

N = number of trials = 30

R = desired success

A)

P(0) = 30c0*(0.04^0)*(1-0.04)^30-0 = 0.29385764323

B)

P(5) = 0.00525913032.

C)

P(0) + P(1) + P(2) = 0.88310343825.

D)

P(0) + P(1) + P(2) + P(3) = 0.9694071153.

E)

P(at least 1) = 1 - P(0) = 0.70614235677

F)

P(greater than 3) = 1 - [p(0) + p(1) + p(2) + p(3)]

= 0.0305928847

G)

P(1) = 0.36732205404