Question

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

Answer 1

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)

$P(r=0)=^{20}C_0\left ( 0.5\right )^{0}\left ( 0.5\right )^{20}=\left ( 0.5\right )^{20}$

$P(r=1)=^{20}C_0\left ( 0.5\right )^{1}\left ( 0.5\right )^{19}=20\left ( 0.5\right )^{20}$

$P(r=2)=^{20}C_0\left ( 0.5\right )^{2}\left ( 0.5\right )^{18}=190\left ( 0.5\right )^{20}$

$P(r=3)=^{20}C_0\left ( 0.5\right )^{3}\left ( 0.5\right )^{17}=1140\left ( 0.5\right )^{20}$

$P(r=4)=^{20}C_0\left ( 0.5\right )^{4}\left ( 0.5\right )^{16}=4845\left ( 0.5\right )^{20}$

$P(r=5)=^{20}C_0\left ( 0.5\right )^{5}\left ( 0.5\right )^{15}=15,504\left ( 0.5\right )^{20}$

$P(r$

$P(r$

P(r<6)=0.02069