Answer:
Step-by-step explanation:
Let r = .25 probability of getting question right. and w = .75 prob getting it wrong.
[tex]\left ( r+w \right )^{10}[/tex] since there are 10 questions, this will tell us what we want to know.
a) 1-[tex]\left (w\right )^{10}[/tex] doesn't get them all wrong.
1-[tex]\left (0.75\right )^{10}\\[/tex]
=1-.0563
=.9437
b) Probability of getting 6-10 answers right
[tex]\left (r\right )^{10}+10\left ( r \right )^{9}w+45\left ( r \right )^{8}w^{2}+120\left ( r \right )^{7}w^{3}+120\left ( r \right )^{6}w^{4}[/tex]
=.0197
c) This means 9 or 10 answer should be right
[tex]\left (r\right )^{10}+10\left ( r \right )^{9}w[/tex]
=.00003
d) [tex]10\times 0.25[/tex] = 2.5 expected correct answers.
e) Standard deviation for a binomial distribution is [tex]\sqrt{n\ast p\left ( 1-p \right )}[/tex]
=[tex]\sqrt{10\ast0.25\ast0.75}[/tex]
=[tex]\sqrt{1.875}[/tex]
=1.369
