Question

1a) Discuss the importance coefficient of correlation in explaining the relationship between two variables.

b)The chance of any photocopier being defective is 20%. If 15 photocopiers are selected at random, what is the probability that

I)Fewer than 4 will be defective?

ii)None will be defective?

iii) Exactly 6 will be defective?

iv) Between 7 and 9 will be defective?

v)At least 10 will not be defective?

C) Determine the probability of receiving a score greater than 850 on GMAT test that has a mean of 496 and the standard deviation of 116

Answer 1

1a) The correlation coefficient is very important in explaining the strength between the variables for example Pearson correlation measures the strength and direction of a linear relationship between two variables.

b)1) p= 0.2

q= 1-0.2= 0.8

n=15

P(X<4) = P(X= 0, 1, 2, 3)

nCx (p^x)(q^1-x)

15C0*(0.2^0)(0.8^15) + 15C1(0.2^1)(0.8^14) + 15C2(0.2^2)(0.8^13) + 15C3(0.2^3)*(0.8^12)

=0.03518+ 0.1319+ 0.2309+ 0.25014= 0.64812

2) P(X=0)

15C0*(0.2^0)*(0.8^15)

=0.03518

3) P(X=6)

15C6*(0.2^6)*(0.8^9)

=0.04299

4) P (7<X<9) =P(X=8)

15C8*(0.2^8)*(0.8^7)

=0.003455

5) At least 10 will not be defective

Is also the same as at most 5 will be defective

P(x is less or equal to 5)

From roman 1 we have the answer of p(x <4)

=0.64812 + 15C4*(0.2^4)(0.8^11)+ 15C5(0.2^58)*(0.8^10)

  0.64812+ 0.1876+ 0.1032= 0.9389

c)

 Z= (X-mean)/ Standard deviation

P(X>850)

Z= (850-496)/116

P (Z=3.052) = 0.99886

P(X> 850) = 1-0.99886)

=0.00114