A recent study found that 69 % of workers between the ages of 20-29 cash out the
ID: 3307350 • Letter: A
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 e 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?
The probability is _____
(Round to four decimal places as needed.)
b. 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.)
c. What is the probability that 11 or fewer workers cashed out their retirement accounts?
The probability is ______
(Round to four decimal places as needed.)
d. What are the mean and standard deviation for this distribution?
The mean is _____
(Type an integer or a decimal.)
The standard deviation is ____
(Round to four decimal places as needed.)
Explanation / Answer
Let x = workers cashed out their retirement accounts
p = percentag of workers between the ages of 20-29 cash out their retirement accounts = 0.69
q = 1 - p = 1 - 0.69 = 0.31
A ) we want to calculate the probability that probability that exactly 6 workers cashed out their retirement accounts
i.e P(X=6)
By using binomial distribution we can calculate the probabilities
By using excel command we can calculate it as
=BINOMDIST(number , trials , cumulative , probability)
=BINOMDIST(6,14,0.69,FALSE)
= 0.0276
B ) we want to calculate the probability that all 14 workers from the sample cashed out their retirement accounts
i.e P(x=14)
By using excel command we can calculate it as
=BINOMDIST(number , trials , cumulative , probability)
=BINOMDIST(14,14,0.69,FALSE)
=0.05545 ..( Answer)
C ) we want to calculate the probability that 11 or fewer workers cashed out their retirement accounts
i.e P(X<11)
By using excel command we can calculate it as
=BINOMDIST(number , trials , cumulative , probability)
=BINOMDIST(10,14,0.69,TRUE)
=0.6747 ,,,,(Answer)
D ) For Binomial distribution
Mean = n*p = 14*0.69 = 9.66
Variance = n*p*q= 14*0.69*(1-0.69) = 2.9946