Question

1) The yearly amounts of carbon emissions from cars in Belgium are normally distributed with a mean of 13.9 gigagrams per year and a standard deviation of 9.2 gigagrams per year. Find the probability that the amount of carbon emissions from cars in Belgium for a randomly selected year are between 11.5 gigagrams and 14.0 gigagrams per year.

2)   On average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 12.2 inches. Find the probability that a randomly selected part from this supplier will have a value between 87.5 and 107.5 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?

3)  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 118 rotations per minute, would the process be considered in control or out of control?

4)  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, 6.5, 5.0, 4.9, 6.2, 5.1, 5.7, 6.1. Is the process in control or out of control and why?

5)  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?

Answer 1