Question

A soccer team estimates that they will score on 7% of the corner kicks. If this team has 195 corner kicks over the​ season, what are the chances that they score more than 19 times?

Answer 1

Answer)

N = 195

P = 0.07

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 13.65

N*(1-p) = 181.35

Both the conditions are met so we can use standard normal z table to estimate the probability

P(x>19)

By continuity correction

P(x>19.5)

Z = (x - mean)/(s.d/√n)

Mean = n*p = 13.65

S.d = √{n*p*(1-p)} = 3.56293418406

Z = ( x - mean)/s.d

Z = (19.5 - 13.65)/3.56293418406

Z = 1.64

From z table, P(z>1.64) = 0.0505