We are given
Firstly, we can find gradient
so, we will find partial derivatives
now, we can plug point (-5,5,2)
so, gradient will be
now, we are given that
it is in direction of v=⟨−3,2,−4⟩
so, we will find it's unit vector
now, we can find unit vector
now, we can find dot product to find direction of the vector
now, we can plug values
.............Answer
Answer:
The minimum sample size needed is 125.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
For this problem, we have that:
99% confidence level
So , z is the value of Z that has a pvalue of
, so
.
What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?
This minimum sample size is n.
n is found when
So
Rounding up
The minimum sample size needed is 125.
