Questions: The use of drones, aircraft without onboard human pilots, is becoming more prevalent. According to a 2017 report, 57% of people in a certain region had seen a drone in action. Suppose 50 people from this region are randomly selected. Complete parts (a) through (d) below. a. What is the probability that at least 25 had seen a drone? The probability that at least 25 had seen a drone is (Type an integer or a decimal. Round to three decimal places as needed.)

The use of drones, aircraft without onboard human pilots, is becoming more prevalent. According to a 2017 report, 57% of people in a certain region had seen a drone in action. Suppose 50 people from this region are randomly selected. Complete parts (a) through (d) below.
a. What is the probability that at least 25 had seen a drone?

The probability that at least 25 had seen a drone is
(Type an integer or a decimal. Round to three decimal places as needed.)

Transcript text: The use of drones, aircraft without onboard human pilots, is becoming more prevalent. According to a 2017 report, $57 \%$ of people in a certain region had seen a drone in action. Suppose 50 people from this region are randomly selected. Complete parts (a) through (d) below. a. What is the probability that at least 25 had seen a drone? The probahility that at least 25 had seen a drone is $\square$ (Type an integer or a decimal. Round to three decimal places as needed.)

Solution

Solution Steps

Step 1: Define the Problem

We are tasked with finding the probability that at least 25 out of 50 randomly selected people have seen a drone, given that the probability of a person having seen a drone is $ p = 0.57 $.

Step 2: Calculate the Probability of Fewer than 25 Successes

To find the probability of at least 25 successes, we first calculate the probability of having fewer than 25 successes, which is given by:

\[ P(X < 25) = P(X = 0) + P(X = 1) + P(X = 2) + \ldots + P(X = 24) \]

Using the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

where $ n = 50 $ and $ q = 1 - p = 0.43 $.

The calculated probabilities for $ x = 0 $ to $ x = 24 $ are as follows:

$ P(X = 0) = 0.0 $
$ P(X = 1) = 0.0 $
$ P(X = 2) = 0.0 $
$ P(X = 3) = 0.0 $
$ P(X = 4) = 0.0 $
$ P(X = 5) = 0.0 $
$ P(X = 6) = 0.0 $
$ P(X = 7) = 0.0 $
$ P(X = 8) = 0.0 $
$ P(X = 9) = 0.0 $
$ P(X = 10) = 0.0 $
$ P(X = 11) = 0.0 $
$ P(X = 12) = 0.0 $
$ P(X = 13) = 0.0 $
$ P(X = 14) = 0.0 $
$ P(X = 15) = 0.0 $
$ P(X = 16) = 0.001 $
$ P(X = 17) = 0.001 $
$ P(X = 18) = 0.001 $
$ P(X = 19) = 0.003 $
$ P(X = 20) = 0.006 $
$ P(X = 21) = 0.012 $
$ P(X = 22) = 0.021 $
$ P(X = 23) = 0.033 $
$ P(X = 24) = 0.05 $

Step 3: Sum the Probabilities

Now, we sum these probabilities to find $ P(X < 25) $:

\[ P(X < 25) = 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.0 + 0.001 + 0.001 + 0.001 + 0.003 + 0.006 + 0.012 + 0.021 + 0.033 + 0.05 = 0.873 \]

Step 4: Calculate the Probability of At Least 25 Successes

Finally, we calculate the probability of at least 25 successes:

\[ P(X \geq 25) = 1 - P(X < 25) = 1 - 0.873 = 0.127 \]