Godrejy soap manufacturing company was distributing a particular brand of soap through a large number of retail shops. Before a heavy advertisement campaign, the mean sales per week per shop was 140 dozens. After the campaign, a sample of 26 shops was taken and the mean sales was found to be 147 dozens with standard deviation 16. Can you consider the advertisement effective ?

Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2.   Step 2 of 3 :   Compute the value of the test statistic. Round your answer to two decimal places.

The heights of 10 year old American children are normally distributed with a mean height of 4 feet and 5 inches (or 53 inches) and a standard deviation of 4.5 inches.In order to be allowed to go on a particular kids ride at the amusement park, children must be at least 44.9 inches tall and no more than 59.75 inches tall.What percent of 10 year old American children cannot go on the ride?

In a certain country the heights of adult men are normally distributed with a mean of 67.2 inches and a standard deviation of 2.3 inches. The​ country's military requires that men have heights between 64 inches and 75 inches. Determine what percentage of this​ country's men are eligible for the military based on height.