Question

In a certain state office, the amount of time that passes between when a worker submits a reimbursement form and when the reimbursement check is written is normally distributed with a mean of 33 days and a standard deviation of 7 days.

Suppose a random group of 35 reimbursement forms is collected and the mean amount of time it takes to write the reimbursement check is calculated. What is the probability that the mean of this sample will be less than 32 days?

Answer 1

Solution :

Given that,

mean = = 33

standard deviation = =7

n = 35

= 33

=  / n = 7/ 35=1.18

P( <32 ) = P[( - ) / < (32 - 33) /1.18 ]

= P(z < -0.85)

Using z table  

=0.1977   

probability= 0.1977