Answer:

Step-by-step explanation:
The explanation of given question is described below:
Here, the test of hypothesis states that

The test statistic is


= 2.1
According to the given data α = 0.05,
So, the major value is

(refer to the standard normal table)
.
Finally

Answer:
Step-by-step explanation:
This is one minus the probability that all the girls audition for different roles. The total number of ways of assigning roles to the girls is 12^7, because to each of the 7 girls, you have a choice of 12 roles.
Then if each girl is to receive a different role, then there are 12!/5! possibilities for that. If you start assigning roles to the girls, then for the first girl, there are 12 choices, but for the next you have to choose one of the 11 different ones, so 11 for the next, and then one of the 10 remaining for the next etc. etc., and this is 12*11*10*...*6 = 12!/(12-7)! =12!/5!
The probability that a random assignment of one of the 12^7 roles would happen to be one of the 12!/5! roles where each girl has a different role, is
(12!/5!)/12^7 = 12!/(12^7 5!)
Then the probability that two or more girls addition for the same part is the probability that not all the girls are assigned different roles, this is thus:
1 - 12!/(12^7 5!)
Alright, so he has an <em>annual </em>salary of 47,000 dollars. Which means that he is paid 47,000 dollars in 12 months. You'll first have to calculate the pay Vijay receives <em>each month</em>, which is

, or about $3,916.67 (I'll round up to 3917 for simplicity).
Now, he gets paid twice a month. So each paycheck is half of $3917. 3917 x (1/2) = $1958.50.
So each paycheck should be $1958.50 (this is a rounded figure).