A survey was given to a random sample of students attending college in which they were asked, "As a college student, do you feel
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Check the picture below.
based on the equation, if we set y = 0, we'd end up with 0 = 0.5(x-3)(x-k).
and that will give us two x-intercepts, at x = 3 and x = k.
since the triangle is made by the x-intercepts and y-intercepts, then the parabola most likely has another x-intercept on the negative side of the x-axis, as you see in the picture, so chances are "k" is a negative value.
now, notice the picture, those intercepts make a triangle with a base = 3 + k, and height = y, where "y" is on the negative side.
let's find the y-intercept by setting x = 0 now,
now, we can plug those values on A = (1/2)bh,
Part a)
The simple random sample of size n=36 is obtained from a population with
and
The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.
Therefore the sampling distribution has a mean of
The standard error of the means becomes the standard deviation of the sampling distribution.
Part b) We want to find
We need to convert to z-score.
Part c)
We want to find
We convert to z-score and use the normal distribution table to find the corresponding area.
Part d)
We want to find :
We convert to z-scores and again use the standard normal distribution table.