A recent study found that 69% of workers between the ages of 20-29 cash out thei

Question

A recent study found that 69% of workers between the ages of 20-29 cash out their retirement accounts when they lose their jobs or move to a new employer. Complete parts a through d below based on a random sample of 14 workers between the ages of 20-29 who lost their jobs or changed employers.
A.) what is the probability that exactly 6 workers cashed out their retirement accounts?
B.) what is the probability that all 14 workers from the sample cashed out their retirement accounts?
C.) what is the probability that 11 or fewer workers cashed out their retirement accounts?
D.) what are the mean and standard deviation for this distribution? A recent study found that 69% of workers between the ages of 20-29 cash out their retirement accounts when they lose their jobs or move to a new employer. Complete parts a through d below based on a random sample of 14 workers between the ages of 20-29 who lost their jobs or changed employers.
A.) what is the probability that exactly 6 workers cashed out their retirement accounts?
B.) what is the probability that all 14 workers from the sample cashed out their retirement accounts?
C.) what is the probability that 11 or fewer workers cashed out their retirement accounts?
D.) what are the mean and standard deviation for this distribution?
A.) what is the probability that exactly 6 workers cashed out their retirement accounts?
B.) what is the probability that all 14 workers from the sample cashed out their retirement accounts?
C.) what is the probability that 11 or fewer workers cashed out their retirement accounts?
D.) what are the mean and standard deviation for this distribution?

Explanation / Answer

Ans:

Binomial distribution:

n=14,p=0.69

P(x=k)=14Ck*0.69k*0.3114-k

a)P(x=6)=14C6*0.696*0.318=0.0276

b)P(x=14)=14C14*0.6914*0.310=0.0055

c)Refer the prob table below:

P(x<=11)=1-P(x>11)=1-P(x=12)-P(x=13)-P(x=14)

=1-0.1018-0.0349-0.0055

=1-0.1423=0.8577

d)mean=np=14*0.69=9.66

standard deviation=sqrt(14*0.69*(1-0.69))=1.73

x p(x) 0 0.0000 1 0.0000 2 0.0000 3 0.0003 4 0.0019 5 0.0083 6 0.0276 7 0.0703 8 0.1369 9 0.2032 10 0.2261 11 0.1830 12 0.1018 13 0.0349 14 0.0055

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