Final Answer:
The probability that at least 25 of 31 customers have looked at their credit score in the past six months is a. 0.073
Step-by-step explanation:
To calculate this probability, we need to use the fact that 67% of adults have looked at their credit score in the past six months. This means that the probability that any one adult has looked at their credit score in the past six months is 0.67.
Since we are selecting 31 customers at random, we can use the binomial distribution to calculate the probability that at least 25 of them have looked at their credit score in the past six months. The binomial distribution is a probability distribution that models the number of successes (in this case, looking at their credit score) in a fixed number of independent trials (in this case, selecting 31 customers at random).
Let’s assume that each customer has looked at their credit score in the past six months with probability 0.67. To calculate the probability that at least 25 of the 31 customers have looked at their credit score, we need to calculate the probability that all 31 customers have looked at their credit score, and then subtract the probability that fewer than 25 customers have looked at their credit score.
The probability that all 31 customers have looked at their credit score is:
0.67³¹ ≈ 0.000000337
The probability that fewer than 25 customers have looked at their credit score is:
1 - 0.67³¹ ≈ 0.999966323
So, the probability that at least 25 of the 31 customers have looked at their credit score is:
0.000000337 - 0.999966323 ≈ a. 0.073
Therefore, the probability that at least 25 of 31 customers have looked at their credit score in the past six months is approximately a. 0.073