We have to find the domain of the function:
f ( x ) = ln ln ln x
x > 0
ln x > 0
x > 1
and finally: ln ( ln x ) > 0
ln x > 1
x > e
Answer:
Domain is: x ∈ ( e , + ∞ ).
Total of 5 times = 48 + 48 + 49 + 46 + 64 = 255 mins
Goal:
Average = 53 mins
Total = 53 x 6 = 318 mins
6th ride = 318 - 255 = 63 mins
Answer: She needs to attain 63 mins for her 6th ride.
Answer:
Binomial distribution requires all of the following to be satisfied:
1. size of experiment (N=27) is known.
2. each trial of experiment is Bernoulli trial (i.e. either fail or pass)
3. probability (p=0.14) remains constant through trials.
4. trials are independent, and random.
Binomial distribution can be used as a close approximation, with the usual assumption that a sample of 27 in thousands of stock is representative of the population., and is given by the probability of x successes (defective).
P(x)=C(N,x)*p^x*(1-p)^(n-x)
where N=27, p=0.14, and C(N,x) is the number of combinations of x items out of N.
So we need the probability of <em>at most one defective</em>, which is
P(0)+P(1)
= C(27,0)*0.14^0*(0.86)^(27) + C(27,1)*0.14^1*(0.86^26)
=1*1*0.0170 + 27*0.14*0.0198
=0.0170+0.0749
=0.0919
