Question

7. Solar-heat installations successfully reduce the utility bill 60% of the time. What is the probability that at least 9 out of 10 solar-heat installations are successful and will reduce the utility bill? a. 0.0464
b. 0.9432
c. 0.0403
d. 0.8429

Answer 1

@jim_thompson5910

Answer 2

I used a binomial distr. on this problem

Answer 3

yes you'll need to use a binomial cdf

Answer 4

i did and I got 0.9987 but the solution key says it's a)

Answer 5

how did you get 0.9987 ?

Answer 6

oops wrong problem.. I mean 0.09473

Answer 7

i use p = 0.60 and y = 9 and n = 10

Answer 8

which calculator did you use?

Answer 9

I used the 89 and yes I know about nCr(10,9)*p^y*q^(n-y)

Answer 10

That is what I used..

Answer 11

oh shoot I did it over again and got c.

Answer 12

that's the probability of getting exactly 9 out of 10

you aren't considering 8 out of 10, 7 out of 10, etc and then adding them up

Answer 13

sorry I meant to say just 9 out of 10 and 10 out of 10

Answer 14

can I still use the nCr command?

Answer 15

probability of getting exactly 9 out of 10 = 0.0403
probability of getting exactly 10 out of 10 = x

the answer will be equal to `0.0403 + x`

Answer 16

oh okay i see

Answer 17

got it 0.04636

Answer 18

so we are looking at the ones that failed?

Answer 19

`so we are looking at the ones that failed? ` what do you mean?

Answer 20

you should get 0.0463574016 which rounds to 0.04636

Answer 21

I am sorry I got that but i rounded. nvm about my statement above it doesn't make sense. why do we look at 9 out of 10 and 10 out of 10?

Answer 22

`at least 9 out of 10` = (exactly 9 out of 10) + (exactly 10 out of 10)

Answer 23

saying "at least 9" means we have 9 or more

so we have 9 or we have 10. We can't have any more than 10 because n = 10 is the sample size

Answer 24

I see so P(Y>=9)

Answer 25

correct

Answer 26

\(\Large P(Y \ge 9)\) is the same as \(\Large P(Y = 9) + P(Y = 10)\)