Question

A recent study found that 56% 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 e below based on a random sample of 14 workers between the ages of 20-29 who lost their jobs or changed employers.

1. What is the probability that exactly 3 workers cashed out their retirement accounts? The probability is_________. (Round to four decimal places as needed.)
2. What is the probability that all 14 workers from the sample cashed out their retirement accounts? The probability is_________.(Round to four decimal places as needed.)
3. What is the probability that 11 or fewer workers cashed out their retirement accounts? The probability is _________(Round to four decimal places as needed.)
4. What are the mean and standard deviation for this distribution?
   1. The mean is _________(Type an integer or a decimal.)
   2. The standard deviation is ___________. (Round to four decimal places as needed.

Answer 1

Solution:-

We have given that,

p = proportion of workers between age 20-29 cash out their retirement accounts =56%

i.e. p = 0.56

n = sample size = 14

Let define,

X : number of workers between age 20-29 cash out their retirement accounts

Then from above information,

X~Binomial ( n=14, p=0.56 ) distribution

Therefore,pmf of X is,

Mean and standard deviation for this distribution are

#1)What is the probability that exactly 3 workers cashed out their retirement accounts?

----> i.e. we have to find P(X=3) = ?

Therefore,

#2)What is the probability that all 14 workers from the sample cashed out their retirement accounts?

-----> i.e. we have to find P(X=14) =?

#3)What is the probability that 11 or fewer workers cashed out their retirement accounts?

-----> i.e. we have to find P(X<=11) =??

But,

#4)What are the mean and standard deviation for this distribution?

---->

i)Mean:-

ii) Standard deviation:-