NORMAL DISTRIBUTION N( , )
Math 11F Mean and Standard Deviation Name:
The weight in Kilograms of students in a math class were measured and placed in a chart below. Determine the mean and standard deviation for the data.
|53 |91 |105 |82 |63 |71 |115 |
|62 |72 |84 |65 |59 |74 |62 |
Mean
SD
The football coach has created a chart detailing how fast each of his players can run the 40-yard dash. Find the mean and standard deviation for the data.
|Time (s) |Number of |
| |Players |
|0-10 |1 |
|10-20 |5 |
|20-30 |12 |
|30-40 |15 |
|40+ |3 |
Mean
SD
You are the ordering manager for the company you work for and you are required to buy widgets. Company A states that their widgets have a mean length of 6.5 cm with a standard deviation of 0.9 cm. Company B claims that their widgets have a mean length of 6.5 cm and a standard deviation of 0.01 cm.
From which company should you buy your widgets?
Why?
Examine each histogram below. Without doing any calculations determine which set of data is likely to have the greatest standard deviation and which is likely to have the least. Explain your reasoning.
Greatest SD why?
Least SD why?
Math 11F NORMAL DISTRIBUTION
Normal Distribution is symmetrical about the mean and takes the shape of a bell curve
Normal Distribution is defined by its mean (( ) and its standard deviation (( )
Normal distribution represents the probability of all the possible outcomes.
The probabilities of all possible outcomes add up to 1.
Therefore the total area under the bell curve is equal to 100% or 1
The curve approaches the x-axis but never touches it, except at infinity ([pic]).
Normal Distribution obeys the 68-95-99 rule.
The 68-95-99.7 Rule
68% of data falls within 1 standard deviation of the mean (between ( + 1 and ( – 1).
95% of data falls within 2 standard deviation of the mean (between ( + 2 and ( – 2).
99.7% of data falls within 3 standard deviation of the mean (between ( + 3 and ( – 3).
Since the bell curve for normal distribution is symmetrical about the mean, we can use the 68-95-99 rule to determine the probabilities of the individual sections under the curve.
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