Assignment 3 ** PLEASE NOTE: You don’t need to record a video for this assignment** Managing Ashland MultiComm Services 1. If a sample of 50 prospective customers is selected and no free premium...

Question: 1
a. By using the combination formula, we can derive the probability for each case from 0 to 2. The probability of subscription will be computed by dividing 1 by 50, which is 0.02. The probability of no subscription will be 1 minus 0.02, which is 0.98. The following calculations show the overall probability of subscription by less than 3 customers.
P(X<3) = 50C0*(0.02)*0(.98)50-0+ 50C1*(0.02)*(.98)50-1+ 50C2*(0.02)2*(.98)50-2
= 0.9215
= 92.15%
b. The probability of subscription by 0 or 1 customers will be computed similarly as done for less than 3. However, the combination function will be used only for 0 and 1.
The calculations are as follows:
P(X=0 or 1) = 50C0*(0.02)*0(.98)50-0+ 50C1*(0.02)*(.98)50-1
= 0.7357
     = 73.57%
c. The probability of more than 4 customers taking the subscription will be 1 minus the probability of less than 3 customers taking the subscription. Thus, it will be computed as follows:
P(X>4) = 1- P(X<=4)= 0.0032
= 0.32%
d. Probability of subscription for new estimate= 4/50 =0.08
Probability of subscription based on old estimates= 0.01455
The probability in the first case is 4 times higher than that in the previous estimate, the reason may be that previous data is not the exact depiction of the real probability or it is an outlier.
Question 2:
a. One can determine the probability using the binomial distribution. The probability that 0 customers will subscribe is computed as:
P= 50C0*(0.06)0*(.94)50-0
= 1*1*0.0453
= 0.0453 or 4.53%
The probability that 1 customer will subscribe is computed as:
P= 50C1*(0.06)1*(.94)50-1
= 50*0.06*0.048
= 0.1447 or 14.47%
The probability that 2 customers will subscribe is computed as:
P= 50C2*(0.06)2*(.94)50-2
= 1225*0.036*0.051
= 0.2262 or 22.62%
Thus, the probability of less than 3 customers subscribing is the sum of above probabilities, which is 41.62%.
b. One can determine the probability using the binomial distribution. The probability that 0 customers will subscribe is computed as:
P= 50C0*(0.06)0*(.94)50-0
= 1*1*0.0453
= 0.0453 or 4.53%
The probability that 1 customer will subscribe is computed as:
P= 50C1*(0.06)1*(.94)50-1
= 50*0.06*0.048
= 0.1447 or 14.47%
Thus, the probability of 0 or 1 customers subscribing is the sum of above probabilities, which is 19%.
c. One can determine the probability using the binomial distribution. The probability that 0 customers will subscribe is computed as:
P= 50C0*(0.06)0*(.94)50-0
= 1*1*0.0453
= 0.0453 or 4.53%
The probability that 1 customer will subscribe is computed as:
P= 50C1*(0.06)1*(.94)50-1
= 50*0.06*0.048
= 0.1447 or 14.47%
The probability that 2 customers will subscribe is computed as:
P= 50C2*(0.06)2*(.94)50-2
= 1225*0.036*0.051
= 0.2262 or 22.62%
The probability that 3 customers will subscribe is computed as:
P= 50C2*(0.06)3*(.94)50-3
= 19600*0.000216*0.0546
= 0.2311 or 23.11%
Thus, the probability of more than 4 customers subscribing is 1 minus the sum of above probabilities, which is 17.94%.
d. 1. Results of (a): The probability of subscribers subscribing less than 3 channels when no free premium channels are offered is more than the probability of subscribers subscribing the same when 2 free premium channels are being...