(a)
The binomial distribution can be used because the current situation satisfies all of the following:
1. The probability of success (p=85%) is known and remains constant during the whole experiment
2. The number of trials (n=40) is known and constant.
3. Each trial is a bernoulli trial (success or failure only)
4. All trials are (assumed) independent of each other.
The probability of x successes is therefore
P(X=x)=C(n,x)(p^x)(1-p)^(n-x)
(b) P(X=35) means the probability of 35 successes out of 40 trials at p=0.85
and
P(X=35)=C(40,35)*0.85^35*0.15^5=658008*0.003386*0.00007594
=0.16918
(c) P(X>=35)=∑ P(X=i) for i=35 to 40
=0.16918+0.13315+0.08157+0.03649+0.01060+0.00150
=0.4325
(d) P(X<20)=∑ P(X=i) for i=0 to 19
=0.00000003513 (individual probabilities are very small).
okay so i assume you meant these two:
y=-382 and y=6x+3
Answer:
y=-382
x=-385/6
Step By Step:
y=−382;y=6x+3
Step: Solve y=−382 for y:
y=−382
Step: Substitute −382 for y in y=6x+3:
y=6x+3
−382=6x+3
−382+−6x=6x+3+−6x (Add -6x to both sides)
−6x−382=3
−6x−382+382=3+382 (Add 382 to both sides)
−6x=385
Divide both sides by -6.
x=-385/6
y=-382
You can see it's a geometric sequence because the ratio is constant (
).
The nth term of a geometric sequence:
It has to be the sum for term 4 through term 15, so n=4 and the number above the sigma is 15.
Your answer:
You would have 21.29 dL or rounded up 21.3 dL.
