The approximate probability that more than 92 out of 158 software users will not call technical support is 0.4602, rounded to four decimal places.
Approximating the probability using normal distribution
Here's how we can calculate the probability:
1. Define variables:
n = 158 (number of software users)
p = 0.58 (probability of a user not calling technical support)
q = 1 - p = 0.42 (probability of a user calling technical support)
x = 92 (number of users not calling technical support)
2. Calculate the mean and standard deviation:
Mean (μ) = np = 158 * 0.58 = 91.44
Standard deviation (σ) = sqrt(npq) = sqrt(158 * 0.58 * 0.42) = 5.8
3. Convert x to a z-score:
z = (x - μ) / σ = (92 - 91.44) / 5.8 = 0.1
4. Find the area above z = 0.1 using the standard normal distribution table or calculator:
Area = 0.5398
5. Since we're interested in the probability of more than 92 users not calling, we need to add the area to the right of z = 0.1 to 1:
Probability = 1 - 0.5398 = 0.4602
Therefore, the approximate probability that more than 92 out of 158 software users will not call technical support is 0.4602, rounded to four decimal places.
Complete question:
Consider the probability that more than 92 out of 158 software users will not call technical support. Assume the probability that a given software user will not call technical support is 58%. Approximate the probability using the normal distribution. Round your answer to four decimal places.