Question 1199907: 66% of all violent felons in the prison system are repeat offenders. If 45 violent felons are randomly selected, find the probability that
( I just need help on letter C, the rest I got them correct)
a. Exactly 29 of them are repeat offenders.
0.1205286384
Correct
b. At most 29 of them are repeat offenders.
0.4682375156
Correct
c. At least 30 of them are repeat offenders. ?
d. Between 27 and 31 (including 27 and 31) of them are repeat offenders.
0.553313931
Correct
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
I'll focus on part (c) only.
For questions like this, you could calculate by hand.
However that is tedious busy-work in my opinion. The reason why I say this is because you would have 16 separate calculations, each of which are somewhat long in their own right.
It's better to use a specialized binomial distribution calculator such as this one
https://www.gigacalculator.com/calculators/binomial-probability-calculator.php
In this case:
n = 45 = sample size
p = 0.66 = probability of a repeat offender
x = 30 = number of repeat offenders
Look for where it says "Probability of X ≥ 30 events".
If you want to use your TI83 or TI84 calculator, then refer to this page for more information
https://www.statology.org/binomial-probabilities-ti-84-calculator/
Focus on the binomialcdf function and NOT the binomialpdf.
That page explains how to find the binomialcdf function. Also there are examples.
Something like
binomialcdf(45,0.66,29)
will calculate the sum of the probability values from x = 0 to x = 29
Subtract that from 1 to find the sum of the probabilities from x = 30 to x = 45.
This is valid because
P(0 ≤ X ≤ 29) + P(30 ≤ X ≤ 45) = 1
Therefore you'll type into the TI83 or TI84 calculator 1-binomialcdf(45,0.66,29) to find the probability of having at least 30 repeat offenders.
Be careful to avoid typing in 1-binomialcdf(45,0.66,30) as that would slightly be off.
If instead you want to use a spreadsheet, then the command is called BINOMDIST
https://support.microsoft.com/en-us/office/binomdist-function-506a663e-c4ca-428d-b9a8-05583d68789c
There are many other options.
Let me know if you have any questions about a particular piece of software, website, spreadsheet, or calculator.
Hint about the final answer: It is between 0.5 and 0.6
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