1. Find the z-score for which the area (probability) under the standard normal curve to its left is .40
2. Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation of .070 g. A vending machine will only accept coins weighing between 5.48 and 5.82 g what percent of quarters will be rejected?
3. Find the area (probability) under the standard normal curve that lies either to the left of 1.56 or to the right of 2.3 is
4. Find the area (probability) under the standard normal curve that lies between -2.54 and -1.54
5. The variable x is normally distributed. The mean of x is 60 and the standard deviation of x is 4 find p(x>53)
6. IQ test scored are normally distributed with a mean of 96 and a standard deviation of 11. An individual's IQ score is found to be 100. Find the z score corresponding to this value.
7. The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?
8. Suppose that the replacement times for macing machines are normally distributed with a mean of 10.7 years and a standard deviation of 1.5 years. Find the 82nd percentile of the replacement time distribution.
9. A physical fitness association is including the mile run in its secondary school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 40 seconds. Between what times do we expect 95% of the boys to run the mile?
10. The board of examiners that administer the real estate broker's examination in a certain state found that the mean score on the test was 579 and the standard deviation was 72. If the board wants to set the passing score so that only the best 10% of all applicants will pass, what is the passing score? Assuming that all score are normally distributed.
Can someone please show me how to do these?