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)

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 6 1 12 2 18 3 24 4 40

Mean & Standard Deviation Section 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?

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.

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

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

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

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

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

Apgar scores – Calculate the standard deviation 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

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

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

Homework Worksheet