Question

Please solve and explain steps

suppose 82% o all students aking a beginning p oaramming course fail to get her first program to run on firs subr his on. Con from the other and the chance each student fails on their first try is consistent. (Round answers to three decimal places.) er a group of such student nere e c students succes independent (a) If X is the number of students whose program fails on the first run, then X comes from a binomial distribution with: The binomial probability mass function is: Use this function to calculate probabilities. You may verify the outcome of the function using the R command dbinom(x,n,p) (b) What Is the probablity exactly 4 fail on their first submissions? (c) What is the probability 4 or less fail on their first submissians? (d) What is the probability at least 4 fail on their first submissions? (e) How many students should be expected to fail? ",- (f) What is the standard deviation? Ox- Hint: Find the P(XSx) in R using pbinamfx,n,p)

Answer 1

a.)n=5 p=0.82

b.)

$given P(X=x)=\binom{n}{x}p^x(1-p)^n^-^x$

$given P(X=4)=\binom{5}{4}0.82^4(1-0.82)^5^-^4$

  

c.)

$P(X\leqslant 4)=1-P(X=5))$

   $=1-\binom{5}{5}0.82^5(1-0.82)^5^-^5$

$=1-0.3707$

$=0.629$

d.)

$P(X\geqslant 4)=P(X=4)+P(X=5)$

= $=\binom{5}{4}0.82^4(1-0.82)^5^-^4+\binom{5}{5}0.82^5(1-0.82)^5^-^5$

   $=0.7776=0.778$

e.)

$E(x)=np$

$=5*0.82$

   $=4.1$

f)

$(\sigma )x=\sqrt{n*p*(1-p)}$

   $(\sigma )x=\sqrt{5*0.82*0.18}$

= $=0.859$