Support call times at a technical support center are normally distributed with a mean time of 5 minutes and 30 seconds and a standard deviation of 1 minute and 20 seconds.

i. How many calls are likely to last more than 7 minutes?

ii. A study of data collected at a light bulb factory shows that a batch of 7000 light bulbs has a mean life of 900 hours with a standard deviation of 80 hours. Assuming a normal distribution, estimate how many bulbs will fail before 800 hours.

In the first scenario, we are dealing with a normally distributed set of call times at a technical support center. Given a mean time (μ) of 5 minutes and 30 seconds (which can be converted to 5.5 minutes) and a standard deviation (σ) of 1 minute and 20 seconds (which can be converted to 1.33 minutes), we need to find the proportion of calls that last more than 7 minutes.

Using the z-score formula: z = (x - μ) / σ, where x is the value (7 minutes) we want to find the proportion for, we calculate the z-score as follows: z = (7 - 5.5) / 1.33 ≈ 1.13.

Looking up the z-score in a standard normal distribution table or using a calculator, we find that the proportion of calls lasting more than 7 minutes is around 0.869, which is approximately 21.81%.

For the second scenario, with a batch of 7000 light bulbs and a mean life (μ) of 900 hours and a standard deviation (σ) of 80 hours, we want to estimate the number of bulbs that will fail before 800 hours.

Again, using the z-score formula: z = (x - μ) / σ, where x is the value (800 hours) we want to find the proportion for, we calculate the z-score as follows: z = (800 - 900) / 80 ≈ -1.25.

Consulting the standard normal distribution table or a calculator, we find that the proportion of bulbs failing before 800 hours is around 0.1056. Multiplying this proportion by the total number of bulbs (7000) gives an estimate of approximately 1402 bulbs failing before 800 hours.

Learn more about technical support center.

brainly.com/question/33660862

#SPJ11