1. Question 1 A normal distribution has a mean of 12.7 and a standard deviation of 1.3 Find (a)P (X > 14.2) (b)P ( 8 < X < 10) (c)The 73 rd percentile

2. Question 1 A normal distribution has a mean of 12.7 and a standard deviation of 1.3 Find (a)P (X > 14.2) 0.12428 (b)P ( 8 < X < 10) 0.01875 (c)The 73 rd percentile 13.4967

3. Question 2 A normal distribution has a mean of 29 and a standard deviation of 4 Find (a)P (X < 22) (b)P ( 25 < X < 33) (c)The 10 th percentile

4. Question 2 A normal distribution has a mean of 29 and a standard deviation of 4 Find (a)P (X < 22) 0.04006 (b)P ( 25 < X < 33) 0.68269 (c)The 10 th percentile 23.8738

5. Question 3 A normal distribution has a mean of 132 and a standard deviation of 0.2 Find (a)P (X > 132.1) (b)P ( 131.7 < X < 132.05) (c)The 99 th percentile

6. Question 3 A normal distribution has a mean of 132 and a standard deviation of 0.2 Find (a)P (X > 132.1) 0.30854 (b)P ( 131.7 < X < 132.05) 0.53190 (c)The 99 th percentile 132.4653

7. Question 4 Find the shaded area (mean = 18; standard deviation = 3)

8. Question 4 Find the shaded area (mean = 18; standard deviation = 3) 0.47190

9. Question 5 The median of a Normal distribution is 30, and 66% of the results lie between 24 and 36 (a)State the mean (b)Estimate the standard deviation

10. Question 5 The median of a Normal distribution is 30, and 66% of the results lie between 24 and 36 (a)State the mean 30 (b)Estimate the standard deviation 6

11. Question 6 The mode of a Normal distribution is 90, and 95% of the results lie between 80 and 100 (a)State the mean (b)Estimate the standard deviation

12. Question 6 The mode of a Normal distribution is 90, and 95% of the results lie between 80 and 100 (a)State the mean 90 (b)Estimate the standard deviation 5

13. Question 7 The lifetime of lightbulbs follows a Normal Distribution with mean of 1200 hours and standard deviation of 100 hours (a)What is the minimum time you would you expect at least 80% of the bulbs to last? (b)How many bulbs from a batch of 10000 would have failed after 1000 hours?

14. Question 7 The lifetime of light bulbs follows a Normal Distribution with mean of 1200 hours and standard deviation of 100 hours (a)What is the minimum time you would you expect at least 80% of the bulbs to last? 1115.84 (b)How many bulbs from a batch of 10000 would have failed after 1000 hours? 227.5

15. Question 8 Scores on an exam follow a Normal Distribution with mean of 45 marks and standard deviation of 12 marks (a)If the top 15% of students get an A, what is the grade boundary for an A? (b)If the mean goes up by 3 marks, but the grade boundary stays the same, what percentage of students would get an A?

16. Question 8 Scores on an exam follow a Normal Distribution with mean of 45 marks and standard deviation of 12 marks (a)If the top 15% of students get an A, what is the grade boundary for an A? 57.44 (57) (b)If the mean goes up by 3 marks, but the grade boundary stays the same, what percentage of students would get an A? 22.66%