Question

In a recent study, 14% of people have 20-20 vision. Using a fixed number of trials of 10 individuals, find the following for the Binomial distribution:

a) What is the probability that exactly 2 of the 10 individuals have 20-20 vision? Note: You must show your equation work but you may use your calculator for finding the number of ways of fulfilling the condition. Round answer to 3 decimal places.

b) State the mean, , and the standard deviation, , for this Binomial distribution. Round the standard deviation to 3 decimal places.

Answer 1

Answer:

p=14%=0.14, n=10

a)

x=2

formula for the probability of binomial disribution is

P(X=x) = nCx * Px * (1 - p)n-x

P(X = 2) = 10C2 * 0.142 * ( 1 - 0.14)10-2

P(X = 2) = 45 * 0.0196 * 0.2992179271

P(X = 2) = 0.2639

Probability = 0.264

b)

mean = n * p

mean = 10 * 0.14

mean = 1.4

standard deviation =

standard deviation =

standard deviation = 1.097