Normal Approximation

Answer the following questions

1. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last less than 7 months.Round to the nearest thousandth.

2. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months.Find the probability that an instrument produced by this machine will last between 7 and 12 months. Round to the nearest thousandth.

3. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find how long an instrument that separates the bottom 83.398% will last? Round to the nearest hundredth.

4. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. What is the probability that the average number of months that these 100 instruments will last is greater than 12.2 months? Round to the nearest thousandth.

5. A die is rolled 360 times. If you want to use normal approximation to find the probability that the number of 4 was rolled at least 100 times,what is the mean of the normal distribution that you would use in this case.