Certainly! Let's solve this step-by-step to find the probability that at least 6 out of 8 adult smartphone users use their smartphones in meetings or classes.
### Step 1: Understand the Problem
We are given:
- The probability that an adult smartphone user uses their phone in meetings, [tex]\( p = 0.55 \)[/tex].
- The number of adults selected, [tex]\( n = 8 \)[/tex].
- We need to find the probability that at least 6 of these 8 adults use their smartphones in meetings.
### Step 2: Specify What You Need to Find
We need to calculate the probability that at least 6 out of 8 adults use their smartphones in meetings. This can be expressed in terms of binomial probability:
[tex]\[ P(X \geq 6) \][/tex]
This can be broken down into the sum of probabilities of exactly 6, exactly 7, and exactly 8 adults using their smartphones:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) \][/tex]
### Step 3: Calculate Each Probability
1. Probability of exactly 6 using smartphones:
[tex]\[ P(X = 6) = 0.1569 \][/tex]
2. Probability of exactly 7 using smartphones:
[tex]\[ P(X = 7) = 0.0548 \][/tex]
3. Probability of exactly 8 using smartphones:
[tex]\[ P(X = 8) = 0.0084 \][/tex]
### Step 4: Sum these Probabilities
Add the probabilities of exactly 6, 7, and 8 to get the probability of at least 6:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) \][/tex]
[tex]\[ P(X \geq 6) = 0.1569 + 0.0548 + 0.0084 \][/tex]
[tex]\[ P(X \geq 6) = 0.2201 \][/tex]
### Step 5: Round to Four Decimal Places
The probability of at least 6 out of 8 smartphone users using their smartphones in meetings or classes is [tex]\( 0.2201 \)[/tex] when rounded to four decimal places.
### Final Answer:
The probability that at least 6 out of 8 adult smartphone users use their smartphones in meetings or classes is [tex]\(\boxed{0.2201}\)[/tex].
