1 A brand name has a 50 recognition rate Assume the owner o

1. A brand name has a 50 % recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 4 randomly selected consumers.

Part A: What is the probability that exactly 3 of the selected consumers recognize the brand name? The probability that exactly 3 of the 4 consumers recognize the brand name is:

2.In a clinical trial of a cholesterol drug, 222 subjects were given a placebo, and 9 % of them developed headaches. For such randomly selected groups of 222 subjects given a placebo, identify the values of n, p, and q that would be used for finding the mean and standard deviation for the number of subjects who develop headaches.

The value of n is:

Solution

1.

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 =    4      
p = the probability of a success =    0.5      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.25 [answer]

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2.

n = the number of participants = 222

p = the probability of headaches = 0.09

q = 1 - p = 0.91 [ANSWERS]