normal dist day 4.notebook · 2014. 1. 15. · normal dist day 4.notebook january 15, 2014 normal...

normal dist day 4.notebook January 15, 2014

Normal Probability

Distributions

day 4: Finding Values using the Normal Distribution

WARM UP!

1. The standard normal distribution table (ztable) gives you the area under the ___________ curve that falls to the _______ of the zscore.

2. As the zscores increase (1.00, 1.10, 1.20, 1.30, ...), the cumulative areas under the normal curve_____________.

3. Find the area under the normal curve to the right of z = 0.33.

4. Find the area under the bell curve to the left of z = 2.55.

5. A normal distribution of women's heights has a mean of 63.3 inches and a standard deviation of 2.5 inches. Mrs. Cole's height has a standardized score of z = 2.28.

a. What is her height, in inches? b. What proportion of women are taller?

answers next slide


WARM UP!

1. The standard normal distribution table (ztable) gives you the area under the ___________ curve that falls to the _______ of the zscore.

2. As the zscores increase (1.00, 1.10, 1.20, 1.30, ...), the cumulative areas under the normal curve_____________.

3. Find the area under the normal curve to the right of z = 0.33.

4. Find the area under the bell curve to the left of z = 2.55.

5. A normal distribution of women's heights has a mean of 63.3 inches and a standard deviation of 2.5 inches. Mrs. Cole's height has a standardized score of z = 2.28.

a. What is her height, in inches? b. What proportion of women are taller?

answers

normalleft

increase

1 - 0.6293 = 0.3707

0.0054

0.011369 inches (5'9")

PERCENTILESPERCENTILES

50% of the

Population

50% of the

Population

0 +1 +2 +3123

**When you look up z = 0 on your z‐table, you'll notice you get 0.5, or 50% that is to the left of 0.



0 +1 +2 +3123

0.1587

**When you look up z = ‐1.00 on your z‐table, you'll notice you get 0.1587, or 15.87% that is to the left of 85.


0 +1 +2 +3123

0.8413

**When you look up z = 1.00 on your z‐table, you'll notice you get 0.8413, or 84.13% that is to the left of 115.



0 +1 +2 +3123

0.9772

**When you look up z = 2.00 on your z‐table, you'll notice you get 0.9772, or 97.72% that is to the left of 130.

Find the zscore that corresponds to each percentile.

1. P5 2. P50



3. P90 4. P20


5. P99 6. P10You Try!


Practice & Turn In to Teacher

1. P1 2. P15 3. P40 4. P55

5. P88 6. P96 7. P25 8. P75

9. P35 10. P65

50

Suppose μ = 50 yard line and σ = 10 yards.

1. If you ran +2.00 standard deviations from the mean, on what yard line would that place you? Right or left side of the 50?

2. If you ran 3.00 standard deviations from the mean, on what yard line would that place you? Right or left side of the 50?

3. If you ran +2.25 standard deviations from the mean, on what yard line would that place you? Right or left side of the 50?


Transforming a z‐score into an x‐value (data value)

Solve for x


Finding a Specific xValue:The speeds of boats in Bikini Bottom along the road that runs in front of the Krusty Krab are normally distributed with a mean of 56 mph and a standard deviation of 4 miles per hour. Find the speeds that correspond to the following zscores: 1.96, 2.33, and 0.

*inverse normal



Finding a Specific DATA Value:Scores for a civil service exam (such a a postal office) are normally distributed with a mean of 75 and standard deviation of 6.5. To be eligible for employment, you must score in the top 5%. What is the lowest score you can earn and be eligible for employment?

Finding a Specific DATA Value:You sell a brand of automobile tire that has a life expectancy that is normally distributed with a mean life of 30,000 miles and sd of 2500 miles. You want to give a guarantee for free replacement of tires that don't wear well (in other words, they wear out early). How should you word your guarantee if you are willing to replace approximately 10% of the tires you sell?



Finding a Specific DATA Value:A vending machine dispenses coffee into an 8ounce cup. The amount of coffee dispensed follows a normal distribution with a standard deviation of 0.03 ounce. You can allow the cup to overfill only 1% of the time. What amount should you set as the mean amount of coffee to be dispensed?


Next Class:Independent

PracticeTest

the class after that!

normal dist day 4.notebook · 2014. 1. 15. · normal dist day 4.notebook january 15, 2014 normal...

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