SOLUTION: Assume that one adult with smart phones are renewly selected 41% use them in meetings or class. If 6 adult smartphone users are randomly selected find the probability that at least

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Question 1196891: Assume that one adult with smart phones are renewly selected 41% use them in meetings or class. If 6 adult smartphone users are randomly selected find the probability that at least 4 of them use their smart phone in meetings or classes.
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13198) (Show Source):
You can put this solution on YOUR website!

Look at what you are going to post before you post it....

Your first sentence is garbled, making it impossible to know what the question is.

Re-post correctly....

Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!

When I searched out part of your problem, I came across this exact wording "Assume that when adults with smartphones are randomly selected, 51% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes."

I'll assume that your problem fits a similar format.

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Question:
Assume that when adults with smartphones are randomly selected, 41% use them in meetings or classes. If 6 adult smartphone users are randomly selected find the probability that at least 4 of them use their smart phone in meetings or classes.

Solution:
n = 6 = sample size
p = 0.41 = probability someone uses a smartphone in meetings or in class

Let's consider the case where exactly x = 4 people use a smartphone during meetings or in class
Use the nCr combination formula to find that 6C4 = 15

The scratch work is shown below
n C r = (n!)/(r!(n-r)!)
6 C 4 = (6!)/(4!*(6-4)!)
6 C 4 = (6!)/(4!*2!)
6 C 4 = (6*5*4!)/(4!*2!)
6 C 4 = (6*5)/(2!)
6 C 4 = (6*5)/(2*1)
6 C 4 = (30)/(2)
6 C 4 = 15
There are 15 ways to select four from a pool of six, where order doesn't matter.

Then use the binomial distribution formula
P(x) = (n C x)*(p)^(x)*(1-p)^(n-x)
P(4) = (6 C 4)*(0.41)^(4)*(1-0.41)^(6-4)
P(4) = (6 C 4)*(0.41)^(4)*(0.59)^(2)
P(4) = (15)*(0.41)^(4)*(0.59)^2
P(4) = (15)*(0.02825761)*(0.3481)
P(4) = 0.147547110615
The probability that exactly 4 people use their phone during meetings or in class is roughly 0.147547110615

Repeat similar steps for x = 5 and x = 6
I'll skip the steps and jump to the results of each
P(5) = 0.041013095154
P(6) = 0.004750104241

Then,

The probability of at least 4 people, out of 6 total in the sample size, using a smartphone during meetings or class is roughly 0.19331031001
When rounding to something like four decimal places, we get roughly 0.1933
Round the answer however your teacher instructs.