1. Suppose we know that test scores have a population mean(u) of 55 and a popula

Question

1. Suppose we know that test scores have a population mean(u) of 55 and a population standard deviation (a) of 10. Answer each of the following: a. Using Chebyshev's Theorem, at least what percentage of scores fall between 35 and 75? b. Using Chebyshev's Theorem, at least what percentage of scores fall between 40 and 70? c. Suppose we know scores follow a bell shaped distribution. Approximately what percentage of scores fall between 35 and 75? 2. Suppose we have the following paired data on variables X and Y X: 2 7 8 9 Y: 21 20 18 15 16 18 16 15 11 10 a. b. c. Sketch a scatter diagram of Y and X. By hand, calculate the covariance and correlation between X and Y.' How would you describe the relationship between X and Y?

Explanation / Answer

Ans:

Given that

mean=55 and standard deviation=10

a)35 and 75 are 2 standard deviations below and above the mean respectively.

So,k=2

Atleast percentage of scores fall between 35 and 55=100*(1-(1/k^2))=100*(1-(1/4))=75%

b)40 and 70 are 1.5 standard deviations below and above the mean respectively.

So,k=1.5

Atleast percentage of scores fall between 40 and 70=100*(1-(1/k^2))=100*(1-(1/2.25))=55.56%

c)Now,normal distribution

z=+/-2

P(-2<z<2)=P(z<2)-P(z<-2)=0.9773-0.0228=0.9545 orr 95.45%

or according to empirical rule,95% of the data falls within 2 standard deviations of the mean.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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