Answer to Question #195105 in Statistics and Probability for fahmida

Question

3. Suppose that the authority of East West University found that 20% of its students withdraw  without completing the introductory statistics course. Assume that 20 students registered for the  course in section 3. a. Compute the probability that two or fewer will withdraw. b. Compute the probability that exactly four will withdraw. c. Compute the probability that more than three will withdraw. d. Compute the expected number of withdrawals.

4. Suppose that in Dhaka, twenty-three percent of automobiles are not covered by insurance. On  a particular weekend, 35 automobiles are involved in traffic accidents. a. What is the expected number of these automobiles that are not covered by insurance? b. What are the variance and standard deviation?

Answer 1

4.

a.

$E[X]=35\cdot0.23=8.05$

b.

$Var[X]=E[X^2]-E[X]^2=0.23\cdot35^2-8.05^2=216.95$

$\sigma=\sqrt{Var(X)}=\sqrt{216.95}=14.73$

3.

Using Binomial distribution:

$P(X=k)=C^k_np^k(1-p)^{n-k}$

$p=0.2,n=20$

a.

$P(X\le2)=P(x=0)+P(x=1)+P(x=2)$

$P(x=0)=0.8^{20}=0.0115$

$P(x=1)=20\cdot0.2\cdot0.8^{19}=0.0576$

$P(x=2)=190\cdot0.2^2\cdot0.8^{18}=0.1369$

$P(X\le2)=0.0115+0.0576+0.1369=0.206$

b.

$P(x=4)=4845\cdot0.2^4\cdot0.8^{16}=0.2182$

c.

$P(X>3)=1-(P(x=0)+P(x=1)+P(x=2)+P(x=3))$

$P(x=3)=1140\cdot0.2^3\cdot0.8^{17}=0.2054$

$P(X>3)=1-(0.0115+0.0576+0.1369+0.2054)=0.5886$

d.

$E[X]=np=20\cdot0.2=4$