Question

Consider the probability that more than 88 out of 158 software users will not call technical support. Assume the probability that a given software user will not call technical support is 57%.

Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answer 1

Solution:

Given that,

P = 0.57

1 - P = 0.43

n = 158

Here, BIN ( n , P ) that is , BIN (158 , 0.57)

According to normal approximation binomial,

X Normal

Mean = = n*P = 90.06

Standard deviation = =n*p*(1-p) = 38.7258

We using continuity correction factor

P(x > a ) = P( X > a + 0.5)

P(x > 88.5) = 1 - P(x < 88.5)

= 1 - P((x - ) / < (88.5 - 90.06) / 38.7258)

= 1 - P(z < -0.25)

= 1 - 0.4013   

= 0.5987

Probability = 0.5987