calculate 1 6 10.00 points According to a report from the Center for Studying He

Question

calculate 1

6 10.00 points According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The Wall Street Journal, June 26, 2008). Suppose eight individuals are randomly selected. a. What is the probability that none will delay or go without medical care? (Round your intermediate calculations and final answer to 4 decimal places.) Probability b. What is the probability that no more than two will delay or go without medical care? (Round your intermediate calculations and final answer to 4 decimal places.) Probability c. What is the probability that at least seven will delay or go without medical care? (Round your intermediate calculations and final answer to 4 decimal places.) Probability d. What is the expected number of individuals who will delay or go without medical care? (Round your answer to 1 decimal place.) Expected number of individuals e. Calculate the variance and the standard deviation for this probability distribution. (Round your intermediate calculations and final answers to 4 decimal places.) Variance Standard deviation

Explanation / Answer

a)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    8      
p = the probability of a success =    0.2      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.16777216 [ANSWER]

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b)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    8      
p = the probability of a success =    0.2      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.79691776 [ANSWER]

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c)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    8      
p = the probability of a success =    0.2      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   6   ) =    0.99991552
          
Thus, the probability of at least   7   successes is  
          
P(at least   7   ) =    8.448*10^-5 [ANSWER]

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d)

E(x) = mean = np =    1.6 [ANSWER]

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e)

variance = np(1-p) =    1.28 [ANSWER]

  
s = standard deviation = sqrt(np(1-p)) =    1.13137085 [ANSWER]

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