Question

probability 10%. n= 50 find between 15 and 18 times.

Answer 1

Solution:

Given that,

P = 0.10

1 - P = 0.90

n = 50

Here, BIN ( n , P ) that is , BIN (50 , 0.10)

then,

n*p = 50*0.10 = 5 5

n(1- P) = 50*0.90 = 45 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 5

Standard deviation = =n*p*(1-p) = 50*0.10*0.90 = 4.5

We using countinuity correction factor

P(b < X < a) = P( b - 0.5 < X < a + 0.5)

P(14.5 < x < 18.5) = P((14.5-5)/ 4.5 ) < (x - ) /  < (18.5 - 5) / 4.5) )

= P(4.478 < z < 6.364)

= P(z < 6.364) - P(z < 4.478)

= 1 - 1

= 0

Probability = 0.000