NORMAL DISTRIBUTION
EXPERIMENT!
Person 1: Looks at clock and says “START” and “STOP” for 5 secondsPerson 2: Hits start and stop on stopwatch when person 1 tells them to
Person 3: Record time, rounded to the nearest 0.1 second, in the table to the right
Switch after 10 trials.
+Enter all data values in the calculator at the front.
+Record alldata values in the frequency graph on the board. / Times
Characteristics of a normal curve:What it looks like:
Examples and Non-Examples:
EMPIRICAL RULE:
Says that if your data follows a normal distribution… /Examples:
The heights of the 880 students at East MeckHigh School are normally distributed with a mean of 67 inches and a standard deviation of 2.5 inches- Draw and label the normal curve.
- 68% of the students fall between what two heights?
- What percent of the students are between 59.5 and 69.5 inches tall?
- Approximately how many students are more than 72 inches tall?
- If a student is 62 inches tall, how many standard deviations from the mean are they?
- If a student is 71 inches tall, how many standard deviations from the mean are they?
- If you pick a student at random, what is the probability that they will be between 62 and 72 inches tall?
- If you pick a student at random, what is the probability they will be between 65 and 69 inches tall?
- What is the probability they will be more than 70 inches tall?
- What is the probability they will be less than 61 inches tall?
- Draw and label the normal curve.
- 95% of the water bottles fall between what two volumes?
- What percent of the bottles have between 1.08 and 1.12 liters?
- Approximately how many bottles of water are filled with less than 1.06 liters?
- If a water bottle has 1.16 liters, how many standard deviations from the mean is it?
- If a water bottle has 1.07 liters, how many standard deviations away from the mean is it?
- If you pick a water bottle at random, what is the probability that it will be between 1.06 and 1.12 liters?
- If you pick a water bottle at random, what is the probability it will be between 1.05 and 1.11 liters?
- What is the probability it will have more than 1.13 liters?
- What is the probability it will have less than 1.04 liters?
Z-Score/Standard Score:
What it is: / How to find it:Example 1:Find z if X = 24, = 29 and = 4.2 / You Try:Find Z if X = 19, μ = 22, and σ = 2.6
To find area under the curve/probability in your calculator:
2ndDistrnormalcdf( minimum z, maximum z)
The temperatures for one month for a city in California are normally distributed with mean = 81 degrees and sd = 6 degrees. Find each probability and use a graphing calculator to sketch the corresponding area under the curve.- P(70 < x < 90)
a.Find: P(65 < x < 85)
- P (x > 95)
HOMEWORK (Complete on a separate sheet of paper and draw a normal curve for each situation FIRST)
Find the missing values:- Z if X = 52, μ = 43, and σ = 3.7
- Z if X = 32, μ = 38, and σ = 2.8
- If a normal conversation is held at about 64 decibels, determine the number of hours during the study that the noise level was this low.
- Determine the percent of the study during which the noise was between 76 decibels and 88 decibels.
The life of a certain brand of AA battery is normally distributed with mean = 8 hours and sd = 1.5 hours. Find each probability.
- The battery will last less than 6 hours
- The battery will last more than 12 hours
- The battery will last between 8 and 9 hours
- A blood cholesterol level below 160 mg/dL, which is considered low and can lead to a higher risk of stroke
- A blood cholesterol level above 240 mg/dL, which is considered high and can lead to a higher risk of heart disease
- A blood cholesterol level between 180 and 200 mg/dL, which is considered normal
Dion commutes 290 miles each week for work. His car averages 29.6 miles per gallon with a standard deviation of 5.4 miles per gallon. Assume that the data are normally distributed.
- Approximate the number of miles that Dion’s car gets a gas mileage of 35 miles per gallon or better.
- For what percentage of Dion’s commute does his car have a gas mileage between 24.2 miles per gallon and 40.4 miles per gallon?