S
SYC
Member
Hi everyone,
Sorry if this is quite easy. I've started doing a paper September 2019 and was stuck on question 1.
The question:
A Survey showed that 40% of investors invest in at least two companies in order to diversify their risk.
Calculate an approximate probability that more than 100 investors have invested in at least two companies in a random sample of 300 investors.
I assumed it was a binomial distribution so the expected number and variance would align to the binomial ones but when it came to using the continuity corrections the mark scheme states:
1 - (phi)((100.5-120)/sqrt(72))
= 1 - (phi)(-2.298)
= (phi)(2.298)
= 0.989
My question is how did they get from 1 - (phi)(-2.298) to (phi)(2.298) ? where did the 1 go and how did -2.298 becomes positive (my assumption is the flip graph? as from the binomial distribution the probability is calculated using Z grid and starts from the mean, I'm confused why the P(X>(or equal)100.5) would be subtracted from 1 instead of adding 0.5 from the other half of the graph?
Thank you in advance!
Sorry if this is quite easy. I've started doing a paper September 2019 and was stuck on question 1.
The question:
A Survey showed that 40% of investors invest in at least two companies in order to diversify their risk.
Calculate an approximate probability that more than 100 investors have invested in at least two companies in a random sample of 300 investors.
I assumed it was a binomial distribution so the expected number and variance would align to the binomial ones but when it came to using the continuity corrections the mark scheme states:
1 - (phi)((100.5-120)/sqrt(72))
= 1 - (phi)(-2.298)
= (phi)(2.298)
= 0.989
My question is how did they get from 1 - (phi)(-2.298) to (phi)(2.298) ? where did the 1 go and how did -2.298 becomes positive (my assumption is the flip graph? as from the binomial distribution the probability is calculated using Z grid and starts from the mean, I'm confused why the P(X>(or equal)100.5) would be subtracted from 1 instead of adding 0.5 from the other half of the graph?
Thank you in advance!