Question

Based on patient records from the past several years, 12% of the patients who visit the emergency room at Mercy Hospital do not have health insurance.

a. What is the probability that exactly one out of the next seven random patients who visit the emergency room at Mercy Hospital will not have health insurance?

Do not round intermediate calculations. Round your answer to four decimal places.

Probability =

   

b. What is the probability that two or more out of the next seven random patients who visit the emergency room at Mercy Hospital will not have health insurance?

Round intermediate probabilities to four decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.

Probability =

c. On average, how many out of every 25 random patients who visit the emergency room at Mercy Hospital will not have health insurance?

Round your answer to two decimal places.

Average number = patients

Answer 1

X ~ Bin(n,p)

Where n = 7 , p = 0.12

P(X) = ⁿC_x * p^x * ( 1 - p)^n-x

a )

P(X = 1) =  ⁷C₁ * 0.12¹ * ( 1 - 0.12)⁶

= 0.3901

b)

P(X >= 2) = 1 - P(X <= 1)

= 1 - [ P(X = 0) + P(X = 1) ]

= 1 - [ ⁷C₀ * 0.12⁰ * ( 1 - 0.12)⁷ + ⁷C₁ * 0.12¹ * ( 1 - 0.12)⁶ ]

= 0.2012

c)

E(X) = np = 25 * 0.12

= 3.00