The next two questions (7 and8) refer to the following:
The weight of bags of organic fertilizer is normally distributedwith a mean of 60 pounds and a standard deviation of 2.5pounds.
7. What is the probability that a random sample of 33 bags oforganic fertilizer has a total weight between 1963.5 and 1996.5pounds?
8. If we take a random sample of 9 bags of organic fertilizer,there is a 75% chance that their mean weight will be less than whatvalue? Keep 4 decimal places in intermediate calculations andreport your final answer to 4 decimal places.
The next two questions (8 and9) refer to the following:
Question 10 and 11
Suppose that 40% of students at a university drive tocampus.
10. If we randomly select 100 students from this university,what is the approximate probability that less than 35% of themdrive to campus?
Keep 6 decimal places in intermediatecalculations and report your final answer to 4 decimal places.
11. If we randomly select 100 students from this university,what is the approximate probability that more than 50 of them driveto campus?
Keep 6 decimal places in intermediatecalculations and report your final answer to 4 decimal places.
12. Suppose that IQs of adult Canadians follow a normaldistribution with standard deviation 15. A random sample of 30adult Canadians has a mean IQ of 112.
We would like to construct a 97% confidence interval for thetrue mean IQ of all adult Canadians. What is the criticalvalue z* to be used in the interval? (You do not need tocalculate the calculate the confidence interval. Simply find z*.Input a positive number since we always use thepositive z* value when calculating confidence intervals.)
Report your answer to 2 decimal places.
