Question

A manufacturer of ceramic blades estimates that 1.25% of all blades produced are too brittle to use.We take a random sample of 400 blades.

Use an appropriate approximation to find the approximate probability that at least 4 blades will be too brittle to use.

Answer 1

Solution:

Given that,

P = 0.0125

1 - P = 0.9875

n = 400

Here, BIN ( n , P ) that is , BIN (400 , 0.0125)

then,

n*p = 400 * 0.0125 = 5 5

n(1- P) = 400 * 0.9875 = 395 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 5

Standard deviation = =n*p*(1-p)   = 4.9375

We using continuity correction factor

P(X a ) = P(X > a - 0.5)

P(x > 3.5) = 1 - P(x < 3.5)

= 1 - P((x - ) / < (3.5 - 5) / 4.9375)

= 1 - P(z < -0.68)

= 1 - 0.2483   

= 0.7517

Probability = 0.7517

The approximate probability that at least 4 blades will be too brittle to use is 0.7517.