The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Total scores on the GMAT are normally distributed and historically had a population standard deviation of 113. The Graduate Management Admission Council (GMAC), who administers the test, claims that the mean total score is 529 . Suppose a random sample of 8 students took the test and their scores are given below:
699, 560, 414, 570, 521, 663, 727, 413

Required:
a. Test the claim that the mean total score is 529 using either the classical approach (i. e., critical values and critical regions) or the P-value approach at the 0.05 level of significance.
b. Construct a 95% confidence interval (C. I.) for the true mean score for the population.
c. Does this interval contain the value reported by GMAC?
d. How many students should be surveyed to estimate the mean score within 25 points with 98% confidence?
e. How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?
f. Compare your answers from questions 5 and 6. What effect does decreasing the confidence level have on the sample size required?

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

246

step-by-step explanation: