The mean cost of getting a four-year college degree in a certain region of the c

Question

The mean cost of getting a four-year college degree in a certain region of the country is $48,600 with a standard deviation of $8,100. Assume costs are normally distributed. The fraction of costs for all graduates in this region that fall within ±$4,000 of the mean cost is? a 0.5284 b 0.4844 0.4246 d 0.3758 10 what fraction of sample means from samples of size n = 16 graduates fall within ±$4,000 from the population mean? a 0.8904 0.9198 0.9398 0.9522 4 11 In repeated sampling of n = 25 graduates, the interval which contains the middle 95% of sample mean costs a $41,615 $55,585 b $42,567 $54,633 C $43,837 $53,363 d $45,425 $51,775

Explanation / Answer

Mean cost of getting degree = = $48600

Standard deviation = = $8100

Fraction which lies between Mean +- 4000 is

(a) Z - values are

Z2 = 4000/8100 = 0.49 and Z1 = -0.49

Pr( -0.49 < Z < 0.49) = (0.49) - (-0.49) = 0.6879 - 0.3121 = 0.3758

Option D is correct.

(b) Now size n = 16

Standard error of the sample mean se = 8100/ sqrt(16) = $ 2025

Now sample mean values are in between +- 4000 of sample mean

Z - values are

Z2 = 4000/2025 = 1.98 and Z1 = -1.98

Pr( -1.98 < Z < 1.98) = (1.98) - (-1.98) = 0.9761 - 0.0239= 0.9522

option d is correct.

(c) n = 25 graduates

95% of sample mean = +- Z95% (/ sqrt(n))

= 48600 +- 1.96 * (8100/ sqrt(25) )

= 48600 +- 1.96 * 1620

= (45425, 51775)

option D is correct

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.