please explain these,

1) A process is normally distributed with a mean of 104 rotations per minute and a standard deviation of 8.2 rotations per minute. If a randomly selected minute has 128 rotations per minute, would the process be considered in control or out of control?

In control as this one data point is not more than three standard deviations from the mean

In control as only one data point would be outside the allowable range

Out of control as this one data point is more than three standard deviations from the mean

Out of control as this one data point is more than two standard deviations from the mean

2) The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10th bar off the production line. The reading points are 5.8, 5.9, 4.9, 5.2, 5.0, 4.9, 6.2, 5.1, 5.7, 6.1. Is the process in control or out of control and why?

It is in control as the values jump above and below the mean

It is out of control as one of these data points is more than 3 standard deviations from the mean

It is in control as the data points more than 2 standard deviations from the mean are far apart

It is out of control as two of these data points are more than 2 standard deviations from the mean

3) The blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 1.3 years. What warranty should be provided so that the company is replacing at most 10% of their blenders sold?

6.5 years

11.2 years

9.9 years

9.5 years

4) A puck company wants to sponsor the players with the 10% quickest goals in hockey games. The times of first goals are normally distributed with a mean of 12.56 minutes and a standard deviation of 4.91 minutes. How fast would a player need to make a goal to be sponsored by the puck company?

6.27 minutes

17.47 minutes

18.85 minutes

7.65 minutes