hello how do I solve #17 with work shown thank you! The Institute for College Ac
ID: 3381078 • Letter: H
Question
hello how do I solve #17 with work shown thank you! The Institute for College Access and Success reported that 67% of college students in a recent year graduated with student loan debt. A random sample of 85 graduates is drawn. Find the mean mu_p. Find the standard deviation sigma_p. Find the probability that less than 60% of the people in the sample were in debt. Find the probability that between 65% and 80% of the people in the sample were in debt. Find the probability that more than 75% of the people m the sample were in debt. Would it be unusual if less than 66% of the people m the sample were in debt?Explanation / Answer
a)
up = 0.67 [ANSWER]
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B)
sigmap = sqrt(p(1-p)/n) = sqrt(0.67*(1-0.67)/85) = 0.05100173 [ANSWER]
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c)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.6
u = mean = 0.67
s = standard deviation = 0.05100173
Thus,
z = (x - u) / s = -1.372502462
Thus, using a table/technology, the left tailed area of this is
P(z < -1.372502462 ) = 0.084953536 [ANSWER]
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d)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 0.65
x2 = upper bound = 0.8
u = mean = 0.67
s = standard deviation = 0.05100173
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.392143561
z2 = upper z score = (x2 - u) / s = 2.548933144
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.347476072
P(z < z2) = 0.994597349
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.647121278 [ANSWER]
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e)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.75
u = mean = 0.67
s = standard deviation = 0.05100173
Thus,
z = (x - u) / s = 1.568574242
Thus, using a table/technology, the right tailed area of this is
P(z > 1.568574242 ) = 0.058373589 [ANSWER]
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f)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.65
u = mean = 0.67
s = standard deviation = 0.05100173
Thus,
z = (x - u) / s = -0.392143561
Thus, using a table/technology, the left tailed area of this is
P(z < -0.392143561 ) = 0.347476072
NO. This is a large probability, it is not unusual. [ANSWER]
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