A local county has an unemployment rate of 6.2%. A random sample of 19 employable people are pick...

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A local county has an unemployment rate of 6.2%. A random sample of 19 employable people are pick...

A local county has an unemployment rate of 6.2%. A random sample of 19 employable people are picked at random from the county and are asked if they are employed. The distribution is a binomial. Round answers to 4 decimal places.

a) Find the probability that exactly 2 in the sample are unemployed.

b) Find the probability that there are fewer than 3 in the sample are unemployed.

c) Find the probability that there are more than 4 in the sample are unemployed.

d) Find the probability that there are at most 3 in the sample are unemployed.

math Statistics-And-Probability

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Answer 1

Answer #1

$X \sim B ( n = 19 , P = 0.062 )$
$P(X = x) = C_{x}^{n} P^{x} Q^{(n-x)}$

part a)

$P(X = 2 ) = C_{ 2}^{ 19} ( 0.062 )^{2} ( 0.938 )^{( 19 - 2 )} = 0.2214$

Part b)

$P(X = 0 ) = C_{ 0}^{ 19} ( 0.062 )^{0} ( 0.938 )^{( 19 - 0 )} = 0.2964$
$P(X = 1 ) = C_{ 1}^{ 19} ( 0.062 )^{1} ( 0.938 )^{( 19 - 1 )} = 0.3722$
$P(X = 2 ) = C_{ 2}^{ 19} ( 0.062 )^{2} ( 0.938 )^{( 19 - 2 )} = 0.2214$
P ( X < 3 ) = 0.8900

Part c)

$P(X = 0 ) = C_{ 0}^{ 19} ( 0.062 )^{0} ( 0.938 )^{( 19 - 0 )} = 0.2964$
$P(X = 1 ) = C_{ 1}^{ 19} ( 0.062 )^{1} ( 0.938 )^{( 19 - 1 )} = 0.3722$
$P(X = 2 ) = C_{ 2}^{ 19} ( 0.062 )^{2} ( 0.938 )^{( 19 - 2 )} = 0.2214$
$P(X = 3 ) = C_{ 3}^{ 19} ( 0.062 )^{3} ( 0.938 )^{( 19 - 3 )} = 0.0829$
$P(X = 4 ) = C_{ 4}^{ 19} ( 0.062 )^{4} ( 0.938 )^{( 19 - 4 )} = 0.0219$
P ( X > 4 ) = 1 - P ( X <= 4 ) \

P ( X > 4 ) = 1 - 0.9948

P ( X > 4 ) = 0.0052

Part d)

$P(X = 0 ) = C_{ 0}^{ 19} ( 0.062 )^{0} ( 0.938 )^{( 19 - 0 )} = 0.2964$
$P(X = 1 ) = C_{ 1}^{ 19} ( 0.062 )^{1} ( 0.938 )^{( 19 - 1 )} = 0.3722$
$P(X = 2 ) = C_{ 2}^{ 19} ( 0.062 )^{2} ( 0.938 )^{( 19 - 2 )} = 0.2214$
$P(X = 3 ) = C_{ 3}^{ 19} ( 0.062 )^{3} ( 0.938 )^{( 19 - 3 )} = 0.0829$
P ( X <= 3 ) = 0.9729

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