Question 1A 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 73rd percentile

Question 1A 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 73rd percentile 13.4967

Question 2A 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 10th percentile

Question 2A 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 10th percentile 23.8738

Question 3A 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 99th percentile

Question 3A 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 99th percentile 132.4653

Question 4Find the shaded area (mean = 18;

standard deviation = 3)

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300

0.05

0.1

0.15

0.2

x

f(x)

Question 4Find the shaded area (mean = 18;

standard deviation = 3)

0.47190

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300

0.05

0.1

0.15

0.2

x

f(x)

Question 5The 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

Question 5The 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

Question 6The 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

Question 6The 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

Question 7The 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?

Question 7The 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

Question 8Scores 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?

Question 8Scores 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%