NORMAL DISTRIBUTION:

1.The Fresha Tea Company pack tea in bags marked as 250 g. A large number of packs of tea were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively. Assuming this data is normally distributed, what percentage of packs are underweight?

2.The ages of the population of a town are Normally distributed with mean 43 and standard deviation 14. The town has a population of 5,000. How many would you expect to be aged between 22 and 57?

3.Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university?

4.In a city, it is estimated that the maximum temperature in June is normally distributed with a mean of 23 and a standard deviation of 5. Calculate the number of days in this month in which it is expected to reach a maximum of between 21 and 27.

5.The marks of 200 candidates in an exam are normally distributed with mean 52 and standard deviation 18. The top 15 % of the candidates are awarded a distinction. Find the mark necessary to gain a distinction

6.The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given.