Question

If 15% of adults in a certain country work from home, what is the probability that fewer than 48 out of a random sample of 400 adults will work from home? (Round your answer to 3 decimal places)

Answer 1

Solution:

Given that,

P = 0.15

1 - P = 0.85

n = 400

Here, BIN ( n , P ) that is , BIN (400 , 0.15)

then,

n*p = 60 > 5

n(1- P) = 340 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 60

Standard deviation = =n*p*(1-p) = 51

We using continuity correction factor

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

P(x < 47.5) = P((x - ) / < (47.5 - 60) / 51)

= P(z < -1.75)

Probability = 0.040