Answer:
1. 77520
2. 
= 0.0017
3. 
= 0.0019
4. 
= 0.9981
5. 
= 0.2036
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n can be calculated as:
So, there are 77520 selections that result in all 7 workers coming from the day shift. It is calculated as:
At the same way, the total number of selections of 7 workers from the 45 is 45C7, so the probability that all 7 selected workers will be from the day shift is:
The probability that all 7 selected workers will be from the same shift is calculated as:
Because the consultant can select all workers from the day shift (20C7) or can select all workers from the swing shift (15C7) or can select all workers from the graveyard shift (10C7).
On the other hand, the probability that at least two different shifts will be represented among the selected workers is the complement of the probability that all 7 selected workers will be from the same shift. So it is calculated as:
Finally, the probability that at least one of the shifts will be un-represented in that sample of workers is:
Where 25C7 is the number of ways to select all 7 workers from swing or graveyard shift, 30C7 is the number of ways to select all 7 workers from day or graveyard shift and 35C7 is the number of ways to selects all 7 workers from day shift and swing shift.
Original cost of the book = $25
Percentage of discount got by Marilyn while buying the book = 15%
Amount of discount got by Marilyn while buying the book = (15/100) * 25
= 375/100
= 3.75 dollars
So
The amount paid by Marilyn for buying the book = (25 - 3.75) dollars
= 21.25 dollars
<span>So the total amount paid by Marilyn for buying the book is $21.25.
I hope the procedure for doing this problem is clear to you.</span>
Answer:
The length RS = 7
Step-by-step explanation:
Here, we are interested in determining the length of RS
Let’s have the line segment arranged as follows;
Q R S
where QR = 9 and QS = 16
From the arrangement, we can deduce that;
QS = QR + RS
Thus;
RS = QS - QR
RS = 16 -9
RS = 7
Answer:
a) 
b) 
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
And 0 for other case. Let X the random variable that represent "life lengths of automobile tires of a certain brand" and we know that the distribution is given by:
The cumulative distribution function is given by:
Part a
We want to find this probability:
and for this case we can use the cumulative distribution function to find it like this:
Part b
For this case w want to find this probability
We have an important property on the exponential distribution called "Memoryless" property and says this:
On this case if we use this property we have this:
We can use the definition of the density function and find this probability:
