United Medicine Inc claims that a drug Viro significantly re

United Medicine, Inc., claims that a drug, Viro, significantly relieves the symptoms of a certain viral infection for 70 percent of all patients. Suppose that this drug is given to 7 randomly selected patients who have been diagnosed with the viral infection.

(a) Let x equal the number of the 7 randomly selected patients whose symptoms are significantly relieved. What distribution describes the random variable x ? (Round your answers to 1 decimal place.) Binomial, n = , p =

(b) Assuming that the company\'s claim is correct, find P(x 5). (Round your answer to 4 decimal places.) P (x 5) =

(c) Suppose that of the 7 randomly selected patients, 5 have had their symptoms significantly relieved by Viro. Based on the probability in part b, would you believe the claim of United Medicine, Inc.?

Solution

a)

it is a binomial distribution with n = 7, p = 0.70.

b)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    7      
p = the probability of a success =    0.7      
x = the maximum number of successes =    5      
          
Then the cumulative probability is          
          
P(at most   5   ) =    0.6705828 [ANSWER]

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c)

Yes, because we have no significant evidence that it isn\'t the case, as the P value is large. So, we believe it.