Section 5.2 Binomial Probabilities. 2 Features of a Binomial Experiment 1.There are a fixed number...
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Transcript of Section 5.2 Binomial Probabilities. 2 Features of a Binomial Experiment 1.There are a fixed number...
![Page 1: Section 5.2 Binomial Probabilities. 2 Features of a Binomial Experiment 1.There are a fixed number of trials, n 2.The n trials are independent and repeated.](https://reader036.fdocuments.us/reader036/viewer/2022083119/5a4d1af57f8b9ab059981501/html5/thumbnails/1.jpg)
Section 5.2
Binomial Probabilities
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Features of a Binomial Experiment
1. There are a fixed number of trials, n2. The n trials are independent and repeated3. Each trial has only two outcomes: success, S, and
Failure, F4. The probability of success is the same for each trial
- Prob. of S = p- Prob. of F = 1 – p = q
5. The goal is to find the probability of r successes out of n trials
![Page 3: Section 5.2 Binomial Probabilities. 2 Features of a Binomial Experiment 1.There are a fixed number of trials, n 2.The n trials are independent and repeated.](https://reader036.fdocuments.us/reader036/viewer/2022083119/5a4d1af57f8b9ab059981501/html5/thumbnails/3.jpg)
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Ex: 1
3 multiple-choice questions. Each question has 4 choices, only one is correct. You randomly choose an answer for each.a)P(success for each question) =
P(failure for each question) =
b) List out all the outcomes and their probabilities:
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Probabilities for Binomial Experiments Formula
n: # of trialsp: probability of successq: probability of failurer : # of success (random variable of interest)
Use it to compute P(1 out of 3 questions correct):
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Ex: 2
59% of Internet users are worried about their email privacy. a) Find P(out of 10 users, 6 are worried).
b) Find P(r ≤ 5).
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Using Binomial Distribution in Calculator2nd Vars (distr) (to find exact # of successes) binompdf(n, p, r) (to find # of success or less) binomcdf(n, p, r)Try: for n = 6 and p = 0.50P (r = 4) =
P(r 4) =
P(r ≥ 4) =
P(r < 4) =
P(r > 4) =
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Ex: 3
Seeds of a hybrid tomato have probability 0.70 of germinating. A biologist plants six seeds.
a.) P(exactly four seeds will germinate)
b.) P(at least four seeds will germinate)
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Ex: 4New eye operation known to restore eyesight of 30% of patients.
A new technique for this surgery was successful for 4 of the patients.
Is the new technique better than the old?
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Can you English?•4 or more•At least 4•No fewer than 4•Not less than 4----------------------------•4 or fewer•At most 4•No more than 4•Does not exceed 4----------------------------•More than 4•Exceeds 4-----------------------------•Fewer than 4•Not as large as 4
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