Questions: (CO 3) Sixty percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 25 of them have looked at their score in the past six months? 0.009 0.987 0.004 0.013

(CO 3) Sixty percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 25 of them have looked at their score in the past six months?
0.009
0.987
0.004
0.013

Transcript text: (CO 3) Sixty percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 25 of them have looked at their score in the past six months? 0.009 0.987 0.004 0.013

Solution

Solution Steps

To solve this problem, we can use the binomial probability formula. We need to calculate the probability of having at least 25 successes (people who have looked at their credit score) out of 31 trials (customers), given that the probability of success on a single trial is 0.60. We can use the cumulative distribution function (CDF) of the binomial distribution to find this probability.

Step 1: Define the Problem

We need to find the probability that at least 25 out of 31 adults have looked at their credit score in the past six months, given that the probability of an adult looking at their credit score is \( p = 0.60 \).

Step 2: Use the Binomial Distribution

The problem can be modeled using the binomial distribution \( B(n, p) \), where \( n = 31 \) and \( p = 0.60 \). We are interested in the probability \( P(X \geq 25) \).

Step 3: Calculate the Cumulative Probability

To find \( P(X \geq 25) \), we use the cumulative distribution function (CDF) of the binomial distribution: \[ P(X \geq 25) = 1 - P(X \leq 24) \] Using the CDF, we find: \[ P(X \leq 24) \approx 0.9874 \]

Step 4: Compute the Final Probability

Subtract the cumulative probability from 1: \[ P(X \geq 25) = 1 - 0.9874 \approx 0.0126 \]