Warm Up May 20th Please pick up the 11-2 Enrichment

sheet from the cart and get started (both sides)

Tougher Probability Carson is not having much luck lately. His car

will only start 80% of the time and his moped will only start 60% of the time. Draw a tree diagram to illustrate the

situation. Use the diagram to determine the chance

thatBoth will startHe has to take his car.He has to take the bus.

Tougher Probability A box contains 3 red, 2 blue and 1 yellow marble.

Draw a tree diagram to represent drawing 2 marbles.

With replacement Without replacement

Find the probability of getting two different colors: If replacement occurs If replacement does not occur

Tougher Probability A bag contains 5 red and 3 blue marbles. Two

marbles are drawn simultaneously from the bad. Determine the probability that at least one is red.

Probability Check1. 13/242. 47/70

5. 1/56. 2/57. 3/58. 4/59. 7/1810.11/1811.5/612.5/9

14. 144π/5000 = .090515.3/625 = .004816.(144π + 24)/5000

= .095317.1-(144π/5000) = .9095

22. a) 1,1 2,1 3,1 4,11,2 2,2 3,2 4,21,3 2,3 3,3 4,31,4 2,4 3,4 4,4

b) 16c) 3/16

Probability & Trials Ch. 19 Dice Simulation

Normal Distribution Bell-shaped curve defined by the mean

and standard deviation of a data set.

Characteristics of a Normal Distribution

What do the 3 curves have in common?

Characteristics of a Normal Distribution

The curves may have different mean and/or standard deviations but they all have the same characteristicsBell-shaped continuous curveSymmetrical about the meanMean, median and mode are the same

and located at the center It approaches, but never touches the x

axisArea under the curve is always 1 (100%)

Is it Normal?

Empirical Rule If data follows a normal distribution…

68% of it will be within 1 standard deviation

95% of it will be within 2 standard deviations

99% of it will be within 3 standard deviations

Empirical Rule

Empirical Rule

Examples The heights of the 880 students at East

Meck High School are normally distributed with a mean of 67 inches and a standard deviation of 2.5 inches

a) Draw and label the normal curve.  

b) 68% of the students fall between what two heights?

Examples (cont.)c) What percent of the students are between

59.5 and 69.5 inches tall?

d) Approximately how many students are more than 72 inches tall?

You Try! A machine used to fill water bottle dispenses

slightly different amounts into each bottle. Suppose the volume of water in 120 bottles is normally distributed with a mean of 1.1 liters and a standard deviation of 0.02 liter.

a) Draw and label the normal curve.b) 95% of the water bottles fall between what

two volumes?c) What percent of the bottles have between

1.08 and 1.12 liters?d) Approximately how many bottles of water are

filled with less than 1.06 liters?

Back to Heights Examplese) If a student is 62 inches tall, how many

standard deviations from the mean are they?

f) If a student is 71 inches tall, how many standard deviations from the mean are they?

Standard DeviationsHow to be more specific…

A standard normal distribution is the set of all z-scores (or z-values). It represents how many standard

deviations a certain data point is away from the mean.

The z-score is positive if the data value lies above the mean and negative if it’s below the mean.

How to find Z-Scores

Examples Find z if X = 24, µ = 29 and σ = 4.2

You Try! Find Z if X = 19, μ = 22, and σ = 2.6

Back to Heights ExamplesMore Specific

e) If a student is 62 inches tall, how many standard deviations from the mean are they?

f) If a student is 71 inches tall, how many standard deviations from the mean are they?

You Try! A machine used to fill water bottle

dispenses slightly different amounts into each bottle. Suppose the volume of water in 120 bottles is normally distributed with a mean of 1.1 liters and a standard deviation of 0.02 liter.

e) If a water bottle has 1.16 liters, how many standard deviations from the mean is it?

f) If a water bottle has 1.07 liters, how many standard deviations away from the mean is it?

Back to Heights Examples The heights of the 880 students at East

Meck High School are normally distributed with a mean of 67 inches and a standard deviation of 2.5 inches

g) If you pick a student at random, what is the probability that they will be between 62 and 72 inches tall?

h) If you pick a student at random, what is the probability they will be between 65 and 69 inches tall?

Area & Probability 2nd DISTR (Vars button) normalcdf(minimum z value, maximum z

value)Back to h) If you pick a student at random,

what is the probability they will be between 65 and 69 inches tall? (remember mean = 67 and SD = 2.5)

More Examples 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.

a. P(70 < x < 90)

More Examples The scores on a standardized test are

normally distributed with mean = 72 and sd = 11. Find each probability and use a graphing calculator to sketch the corresponding area under the curve.

Find: P(65 < x < 85)

You Try Again! A machine used to fill water bottle

dispenses slightly different amounts into each bottle. Suppose the volume of water in 120 bottles is normally distributed with a mean of 1.1 liters and a standard deviation of 0.02 liter.

g) If you pick a water bottle at random, what is the probability that it will be between 1.06 and 1.12 liters?

 h) If you pick a water bottle at random, what

is the probability it will be between 1.05 and 1.11 liters?

What about these? The temperatures for one month for a city

in California are normally distributed with m = 81 degrees and s = 6 degrees. Find P (x > 95)

What about this one? The scores on a standardized test are

normally distributed with mean = 72 and sd = 11. Find P (x < 89)

You Try! The heights of the 880 students at East

Meck High School are normally distributed with a mean of 67 inches and a standard deviation of 2.5 inches

i) What is the probability they will be more than 70 inches tall?

j) What is the probability they will be less than 61 inches tall?

You Try Again! A machine used to fill water bottle

dispenses slightly different amounts into each bottle. Suppose the volume of water in 120 bottles is normally distributed with a mean of 1.1 liters and a standard deviation of 0.02 liter.

i) What is the probability it will have more than 1.13 liters?

j) What is the probability it will have less than 1.04 liters?