Question

1)Assume that when adults with smartphones are randomly selected, 65% use them in meetings or classes. If 8 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in meetings or classes. (5.2.21)

Answer 1

To find the probability of exactly 2 out of 8 adult smartphone users using their smartphones in meetings or classes, you can use the binomial probability formula.

Step-by-step explanation:

To find the probability that exactly 2 out of 8 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula. The formula is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

In this case, n = 8 (number of trials), k = 2 (number of successes), and p = 0.65 (probability of success). Plugging in these values, we get:

P(X=2) = (8 choose 2) * 0.65^2 * (1-0.65)^(8-2)

Calculating this expression gives us the probability of exactly 2 out of 8 adult smartphone users using their smartphones in meetings or classes.

Answer 2

The probability that exactly 7 of the 9 adult smartphone users use their smartphones in meetings or classes is approximately 21.62%.

Define the situation:

We have a binomial experiment with:

n = 9 trials (selecting 9 adults)

p = 0.65 (probability of an adult using smartphone in meetings/classes)

We want the probability of exactly k = 7 successes (adults using smartphones)

Use the binomial probability formula:

The probability of k successes in n trials with probability of success p is:

P(k successes) = (n choose k) * p^k * (1-p)^(n-k)

where:

(n choose k) is the binomial coefficient, representing the number of ways to choose k successes out of n trials. It can be calculated as n! / (k! * (n-k)!).

Calculate the probability:

P(7 successes) = (9 choose 7) * 0.65^7 * (1-0.65)^(9-7)

= 36 * 0.65^7 * 0.35^2

≈ 0.2162