Answer to Question #188261 in Statistics and Probability for Far

Question

The Covid-19 pandemic and its containment measures have led to involuntary job loss and massive reduction in economic activities. Survey data of 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 receive the Prihatin National Aid package. a. What is the probability that 9 package recipients are unemployed? d. Calculate the expected value, the variance, and the standard deviation for the package recipients who are unemployed.

Answer 1

The probability of individuals that are currently unemployed is

$p=\dfrac{28}{60}=0.47,q=1-p=1-0.47=0.53$

$n=15$

(a) The probability that 9 packages recipients are unemplyed is given by-

$P(X=9)=^{15}C_9(0.47)^9(0.53)^6=0.1209$

(b)The probability that at least 12 package recipients are unemployed is given by

$P(X\geq 12) = \sum_{x}^{15} \binom{15}{x}(0.47)^{12}(0.53)^{15-x}$

$P(X\geq 12) = 0.00905$

c)

The probability that 3 or fewer package recipients are unemployed is given by

$P(X\leq 3 ) = \sum_{x=0}^{3} \binom{15}{x}(0.47)^{x}(0.53)^{15-x}$

$P(X\leq 3 ) = 0.0321P(X≤3)=0.0321$

d)

The expected value is given by

$E(X) = np \\ E(X) = 15 \times 0.47\\ E(X) = 7.05$

The variance is given by

$Var(X) = npq \\ Var(X) =15 \times 0.47 \times 0.53 \\ Var(X) =3.7365\\$

The standard deviation is given by

$\sigma =\sqrt{Var(X)}\\ \sigma =1.933$