Question

The sales manager of a small computer company just hired a new sales representative. From experience the manager knows that an average sales representative will make one sale for every 5 customers approached (this is the status quo or null hypothesis). Assume independent customers.

a. if a new employee approaches 5 customers and sells a computer to 4 of them, would you assume that this new employee is significantly better than the average?

b. What is the probability of a different employee selling at least 3 computers under the assumptions of the null hypothesis?

c. What is the probability of a different employee, an average one, selling less than 2 computers?

Answer 1

here this is binomal dstribution with paramter p=1/5=0.2 and n=5

a)

P(selling 4 or more computers)=P(X=4)+P(X=5)=

=0.0064+0.0003 =0.0067

as probability of abve event is less tan 0.05 therefore this is a significant events and we can assume that this new employee is significantly better than the average

b)

P(a different employee selling at least 3 computers under the assumptions of the null hypothesis)

=P(X>=3)=P(X=3)+P(X=4)+P(X=5)

=

=0.0512+0.0064+0.0003=0.0579

c)

probability of a different employee, an average one, selling less than 2 computers

=P(X<2)=P(X=0)+P(X=1)

= =0.3277+0.4096=0.7377