According to u. s. news & world report's publication america's best colleges, the average cost to attend the university of southern california (usc) after deducting grants based on need is $25,050. assume the population standard deviation is $8,200 . suppose that a random sample of 70 usc students will be taken from this population. use z-table. a. what is the value of the standard error of the mean? (to nearest whole number)b. what is the probability that the sample mean will be more than $25,050 ? (to 2 decimals)c. what is the probability that the sample mean will be within $1,250 of the population mean? (to 4 decimals)d. how would the probability in part (c) change if the sample size were increased to 200 ? (to 4 decimals)

a: 980

b: 0.500

c:  0.7994

d:  0.9692

Step-by-step explanation:

For the first situation, we have:

µ = 25,050

σ = 8,200

n = 70

For a:  The standard error is the population standard deviation divided by the square root of the sample size, so

E = 8,200/√70 = 980 (rounded to the nearest whole number from 980.09)

for b:  P(x > 25,050)

Find the z-score for x > 25,050, this will be the area under the curve to the right of 25,050, or

1 - P(x < 25,050).  Find P(x < 25,050)

First find the z-score for this:  z = (25,050 - 25,050)/(8,200/√70) = 0.00

P(z < 0.00) = 0.500

So P(x > 25,050) = 1 - 0.500 = 0.500

For c:  The probability of the sample mean being withing 1,250 gives us a range for the sample mean of 23,800 - 26,300.

See attached photo 1 for the calculations of these z-scores

For d:  We do the same as part c, just change the sample size to 200.  See attached photo 2 for these calculations

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

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step-by-step explanation: