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 8 randomly selectedconsumers. Complete parts (a) through (d) below:
a. What is the probability that exactly 7 of the selected consumers recognize the brand name?
b/ What is the probability that all of the selected consumers recognize the brand name?
c. What is the probability that at least 7 of the selected consumers recognize the brand name? (round to three decimal places)
d. If 8 consumers are randomly selected, is 7 an unusually high number of consumers that recognize the brand name?
A. Yes, because the probability that 7 or more of the selected consumers recognize the brand name is greater than 0.05.
B.No, because the probability that 7 or more of the selected consumers recognize the brand name is greater than 0.05.
C. No because the probability that 7 or more of the selected consumers recognize the brand name is less than 0.05.
D.Yes, because the probability that 7 or more of the selected consumers recognize the brand name is less than 0.05.
a. The probability that exactly 4 of the 5 consumers recognize the brand name is
P(X=7) = (8C7)* (0.50)7 * (0.50)8-7 = 8 * 0.57 * 0.51 = 0.03125 ~ 0.0313
the probability that exactly 7 of the selected consumers recognize the brand name is 0.031.
b. The probability that all of the selected consumers recognize the brand name
P(X =8) = (0.50)8
= 0.0039
The probability that all of the selected consumers recognize the brand name is 0.0039.
c. The probability that at least 4 of the selected consumers recognize the brand name
P( X >=7) = P(X= 7 or X=8)
= 0.0313 + 0.0039
= 0.0352
The probability that at least 4 of the selected consumers recognize the brand name is 0.0352.
d.
Yes, because the probability that 7 or more of the selected consumers recognize the brand name is less than 0.05.
.
A brand name has a 50% recognition rate. Assume the owner of the brand wants to...
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