Answer:
Explanation:
To approximate the probability using the normal distribution, we need to use the mean and standard deviation of the binomial distribution, which can be calculated as follows:
mean = n * p = 153 * 0.13 = 19.89
standard deviation = sqrt(n * p * (1 - p)) = sqrt(153 * 0.13 * 0.87) = 3.41
To use the normal distribution, we need to convert the discrete number of users (fewer than 10) to a continuous range of values. We can do this by subtracting 0.5 from 9.5 to get a range of 9 to 10. Then we use the cumulative distribution function of the standard normal distribution to find the probability of getting a value less than 10, as follows:
z = (10 - mean) / standard deviation = (10 - 19.89) / 3.41 = -2.88
P(Z < -2.88) = 0.002
Therefore, the approximate probability that fewer than 10 out of 153 software users will call technical support is 0.002 (rounded to four decimal places).