1. P(Y≤ 0.4) P(Y < 0.4) P(0.1 < Y ≤ 0.15)
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)

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

3. What about if there were 4 people?

4. Find the mean # born alive
# puppies in a litter born alive
Frequency 6 1 12 2 18 3 24 4 40

5. Mean & Standard Deviation
Section 6.1B

6. Yearbook Ad
Hunger Games

7. 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?

8. 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.

9. Flip 3 coins – what’s the mean number of heads.
x = # heads
p(x) 1 2 3

10. Formula
 𝒙 = 𝒙∙𝒑(𝒙)
It’s also known as the Expected value and is written E(x).

11. Apgar scores – 1 min. after birth and again 5 min
Apgar scores – 1 min. after birth and again 5 min. Possible values are from 0 to 10. Find the mean. x 1 2 3 4 5 6 7 8 9 10
P(x)
0.002
0.001
0.005
0.02
0.04
0.17
0.38
0.25
0.12
0.01

12. What about the standard deviation?
How do you think we find it?

13. Variance: Standard Deviation:
𝜎 2 x= 𝑥−𝜇 2 ∙𝑝(𝑥)

14. Apgar scores – Calculate the standard deviationx 1 2 3 4 5 6 7 8 9 10
P(x)
0.002
0.001
0.005
0.02
0.04
0.17
0.38
0.25
0.12
0.01

15. Find Mean & Standard Deviation:
x = # cars at red light
P(x)
0.13 1
0.21 2
0.28 3
0.31 4
0.07

16. Ex. Find the mean Find the Standard Deviation
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

17. Homework
Worksheet