Answer to Question #146356 in Statistics and Probability for Aysha Zeeshan

Question

Assume that a real estate manager has 5 contacts per week, and she believes that for each contact the probability of making a sale is 0.30. Calculate the following if possible. If any part of question (you feel) is not possible to calculate give reason:
a. Develop the probability distribution table for sale
b. Calculate the expected number of sales per week and variance of sale
c. Find the probability that she makes at most 2 sales.
d. Find the probability that she makes between 3 and 6 sales (both inclusive).

Answer 1

1)p=0.3

q=1-0.3=0.7

P(x=0)=C_5,0*p⁰q^5-0=1*1*0.7⁵=0.16807

P(x=1)=C_5,1*p¹q⁴=1*1*0.7⁵=0.36015

P(x=2)=C_5,2*p²q³=1*1*0.7⁵=0.3087

P(x=3)=C_5,3*p³q²=1*1*0.7⁵=0.1323

P(x=4)=C_5,4*p⁴q¹=1*1*0.7⁵=0.02835

P(x=5)=C_5,5*p⁵q⁰=1*1*0.7⁵=0.00243

Number of sales Probability

0 0.16807

1 0.36015

2 0.3087

3 0.1323

4 0.02835

5 0.00243

2)E(x)=0*0.16807+1*0.36015+2*0.3087+3*0.1323+4*0.02835+5*0.00243=1.5, round to 2.

variance=npq=5*0.3*0.7=1.05

3)P(x≤2)=P(x=0)+P(x=1)+P(x=2)=0.83692

4)there cannot be 6 sales