Question

CO 4) Sixty-seven 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?

0.030

0.970

0.073

0.043

Answer 1

Let X :- Adults Credit score in the past six months

Probability of adults have looked at their credit score in the past six months P = 0.67

Sample Size n = 31

To find the probability

P ( X >= 25 ) = 1 - P ( X < 25)

Using Normal approximation to Binomial continuity correction

P ( X >= 25- 0.5 ) = 1 - P ( X < 25 - 0.5)   

P ( X >= 24.5 ) = 1 - P ( X < 24.5)   

Standardizing the value

P ( X >= 24.5 ) = 1 - P ( Z < 1.42 )

P ( X >= 24.5 ) = 1 - 0.9229

P ( X >= 24.5 ) = 0.0771

Since this probability is calculated using Normal approximation we will see the nearest value of it in the available option, hence 0.073 is closer to this probability

Option 3^rd is correct.