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.

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Presentation transcript:

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

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

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

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

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 ( < X < ) (c)The 99 th percentile

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 ( < X < ) (c)The 99 th percentile

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

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

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

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

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

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

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 would have failed after 1000 hours?

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? (b)How many bulbs from a batch of would have failed after 1000 hours? 227.5

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?

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) (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%