Let Y be a number between 0 and 1 produced by a random number generator. Assuming that the random variable Y has a uniform distribution, find the following probabilities.

• P(Y≤ 0.4)

• P(Y < 0.4)

• P(0.1 < Y ≤ 0.15)

Warm-up

The probability that a person fails the 9th grade is 0.22. Let x = the number of people out of 3 who fail the 9th grade. Write the probability distribution of x.

What about if there were 4 people?

Find the mean # born alive

# puppies in a litter born alive Frequency

0 61 122 183 244 40

MEAN & STANDARD DEVIATIONSection 6.1B

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Mean Value of Random Variable

• Describes where the probability distribution of x is centered.

• Symbol is

• Where do you think the mean is located on the problem we did as a warm-up?

x

Standard Deviation

•Describes the variation of the distribution.

•Symbol is

• If it’s small, then x is close to the mean. If it’s large then there’s more variability.

x

x

Flip 3 coins – what’s the mean number of heads.

x = # heads

p(x)

0

1

2

3

1 3 3 10 1 2 38 8 8 8

3 6 3

8 8 812

81.5

x

x

x

x

18

18

38

38

Formula

• It’s also known as the Expected value and is written E(x).

𝒙=∑ 𝒙 ∙𝒑 (𝒙)

Apgar scores – 1 min. after birth and again 5 min. Possible values are from 0 to 10. Find the mean.

x 0 1 2 3 4 5 6 7 8 9 10

P(x) 0.002 0.001 0.002 0.005 0.02 0.04 0.17 0.38 0.25 0.12 0.01

What about the standard deviation?

•How do you think we find it?

Variance:

Standard Deviation: 2x x

x=

Apgar scores – Calculate the standard deviation

x 0 1 2 3 4 5 6 7 8 9 10

P(x) 0.002 0.001 0.002 0.005 0.02 0.04 0.17 0.38 0.25 0.12 0.01

Find Mean & Standard Deviation:

x = # cars at red light

P(x)

0 0.13

1 0.21

2 0.28

3 0.31

4 0.07

Ex.1. Find the mean2. Find the Standard Deviation3. Find the probability that x is within one

deviation from the mean.

x = possible winnings

P(x)

5 0.1

7 0.31

8 0.24

10 0.16

14 0.19

Homework

• Worksheet