Answer to Question #186659 in Statistics and Probability for Grace

Question

The COVID-19 pandemic and its containment measures have led to involuntary job loss and massive reduction in economic activities. Survey data if a small local community named Julau shows that 28 out of 60 individuals are currently unemployed due to the pandemic outbreak. As part of the initiatives to boost economic recovery, the government has rolled out an economic stimulus package called Prihatin National Aid- a one-off cash assistance for households and individuals in the lower income groups. Suppose that 15 individuals of the Julau community are randomly selected to received the Prihatin National Aid package. 

1. What is the probability that 9 package are unemployed?
2. What is the probability that at least 12 package recipients are unemployed?
3. What is the probability that 3 or fewer package recipients are unemployed?(
4. Calculate the expected value, the variance, and the standard deviation for the package recipients who are unemployed?

Answer 1

The proportion of the unemployed is 28 out of 60=0.4667

Let X be the random variable for the number of unemployed.

n=15

$P(X=x)={n \choose x}p^xq^{n-x}$

1. P(X=9)

$={15\choose 9}0.4667^9*0.5333^6$

=0.1209

1. 2 $P(X\ge12)$

$=\sum_{12}^{15}{15 \choose x}0.4667^x0.5333^{15-x}$

=0.00905

1. 3 $P(X \le3)$

$=\sum_{0}^{3}{15 \choose x}0.4667^x0.5333^{15-x}$

=0.0321

1. 4 Expected value=np

=$15*\frac {28} {60}$

=7

Variance=npq

$=15*\frac{28}{60}*\frac {32}{60}$

=3.733

standard deviation=${\sqrt {\text variance}}$

=$\sqrt {3.733}$

=1.9322