Question

A nuclear reactor facility has two separate safety systems in place to prevent a nuclear meltdown. They prevent meltdown by shutting down the reactor when the temperature reaches the danger level. The first system shuts down the reactor 80% of the time when the danger level is reached. The second system (which is completely separate from the first) shuts down the reactor 90% of the time when the danger level is reached.

a. Use your calculator to do 10 repetitions with the first system alone. Theoretically, it should successfully shut it down 16 out of 20 times.

Answer 1

b. Use your calculator to do 10 repetitions with the second system alone. Theoretically, it should successfully shut it down 18 out of 20 times.
c. Use your calculator to do 20 repetitions with the first and second systems working together. The reactor will successfully shut down if one or both systems are not working.

Answer 2

I don't get any of this...How would I solve it?

Answer 3

I know you have to use randInt on the calculator, but what numbers do I input?

Answer 4

do you have a graphing calculator? like a TI-83 or 84?

Answer 5

Yes, TI-84.

Answer 6

ok
do you know where to find the > and < symbols?

Answer 7

Yes, but that wasn't in my lesson. Just randInt and random digit tables.

Answer 8

ok then
for part a, lets make a table with 10 rows going down, and 3 columns going across
in the first column (on the left) these will be trials (repetitions)
label them 1 to 10 (there are 10 repetitions)
The second column will be where the random numbers go
The third column will be either "yes" or "no" if the reactor stops

to set up the random number generator, use the following function:
randInt(1,10)
then press enter
a random number between 1 and 10 will come up
write this in the second column for each of the 10 trials (you need to do randInt 10 times--you can just press enter repeatedly)

last step: if the number in the second column is less than or equal to 8, write "yes" in the third column. if not, write "no"

post results, lets see what you get

Answer 9

The numbers I got were 4, 8, 10, 10, 7, 7, 1, 2, 8, 4..

Answer 10

since the safety works 8 of 10 times, each trial has an 80% chance of stopping the reactor. since 80% = 8/10, any trial with a number less than or equal to 8 will stop the reactor

Answer 11

So, would I say that? Or would saying that there's a 20% chance of an unsuccessful shutdown?

Answer 12

for every trial with a random less than or equal to 8, the reactor stops. so, next to the random number column, you write "yes" if the number is less than or equal to 8, and "no" otherwise
"yes" and "no" refer to if the safety works or not

Answer 13

okay, but I have four numbers that are a yes.

Answer 14

i count 8 that should be yes, based on the data you gave

Answer 15

Oh, I was counting the 8's and 10's.
4, 8, 10, 10, 7, 7, 1, 2, 8, 4
yes, no, no, no, yes, yes, yes, no, yes ?

Answer 16

Oh i see, the 8's are a yes!

Answer 17

yup. everything (from your data) is a yes except for the 2 tens

Answer 18

Thanks :)! How about c?

Answer 19

you know how to do b?
its the same thing but instead of <=8 you do <=9

for part c, make a table 4 columns across and 20 rows down
the first column (on the left) is the trial number
fill the second column and the 3rd column with random numbers
for the 4th column:
if either the second column is less than/equal to 8 OR the third column is less than/equal to 9, the 4th is a yes
if the second column is either 9 or 10 AND the third column is 10, then write a "no"

Answer 20

Yes, I can do b now. For c, do I also used randInt(1,10 and do 10 trials for both?

Answer 21

it says 20 trials
you do use randInt(1,10)
you're combining the results basically
if one works, great. if not, see if the other one works.
if one works and one doesnt, the safety works
if they both work, then the safety works
if neither work, then the safety doesnt work

Answer 22

So, would I have to have 20 numbers?

Answer 23

you have 40 numbers. 20 trials, and 2 numbers for each trial

Answer 24

3 6
3 8
4 8
5 6
2 2
8 5
6 5
2 4
3 2
2 2
6 3
1 5
3 10
6 3
9 3
9 8
1 9
4 3
9 2
1 10

Answer 25

The numbers I got.

Answer 26

ok
the way to determine if the last column is "yes" (it works) or "no" (it doesnt) is to see if the first one is less than or equal to 8. if it is, the answer is yes. if its not, check if the second column is less than or equal to 9. if it is, the answer is yes. if its not, the answer is no
example
first row
numbers are 3 and 6
the first number is less than/equal to 8, so the answer for that row is "yes"

if it wasnt, check if the second number is less than/equal to 9

btw,
it looks like there arent any that are "no"

Answer 27

Okay, So I would put my results down as the answer?

Answer 28

yes

Answer 29

Okay, thank you so much for helping me :)! I appreciate it.

Answer 30

youre welcome :)