Many people believe that they can tell the difference between Coke and Pepsi. Other people say that the two brands cannot be distinguished. To test this, a random sample of 20 adults was selected to participate in a test. After being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. If people really can't tell the difference, what is the probability that fewer than 6 people will guess correctly

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nuuk nuuk · Answer 1 · 2019-08-05T07:21:14+02:00

Answer:0.0206

Step-by-step explanation:

Using Binomial distribution for a sample of 20 adults

Let r denotes the no of correct answers out of 20

Probability that fewer than 6 people will guess correctly is P(r<6)

P(r<6)=P(r=0)+P(r=1)+P(r=2)+P(r=3)+P(r=4)+P(r=5)

[tex]P(r=0)=^{20}C_0\left ( 0.5\right )^{0}\left ( 0.5\right )^{20}=\left ( 0.5\right )^{20}[/tex]

[tex]P(r=1)=^{20}C_0\left ( 0.5\right )^{1}\left ( 0.5\right )^{19}=20\left ( 0.5\right )^{20}[/tex]

[tex]P(r=2)=^{20}C_0\left ( 0.5\right )^{2}\left ( 0.5\right )^{18}=190\left ( 0.5\right )^{20}[/tex]

[tex]P(r=3)=^{20}C_0\left ( 0.5\right )^{3}\left ( 0.5\right )^{17}=1140\left ( 0.5\right )^{20}[/tex]

[tex]P(r=4)=^{20}C_0\left ( 0.5\right )^{4}\left ( 0.5\right )^{16}=4845\left ( 0.5\right )^{20}[/tex]

[tex]P(r=5)=^{20}C_0\left ( 0.5\right )^{5}\left ( 0.5\right )^{15}=15,504\left ( 0.5\right )^{20}[/tex]

[tex]P(r<6)=\left ( 0.5\right )^{20}\left [ 1+20+190+1140+4845+15504\right ][/tex]

[tex]P(r<6)=\left ( 0.5\right )^{20}\times 21,700[/tex]

P(r<6)=0.02069