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.
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
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