Question

According to the New York State Board of Law Examiners, approximately 64% of people taking the New York Bar passed. Use this information to find the following probabilities. Round solutions to four decimal places, if necessary.

1. If 10 people who have taken the New York Bar are randomly selected, what is the probability that at least 79% have passed? Round your answer to 4 decimal places.
   
   P(ˆp≥0.79)=

• If 42 people who have taken the New York Bar are randomly selected, what is the probability that at least 79% have passed? Round your answer to 4 decimal places.
  
  P(ˆp≥0.79)=

Answer 1

Solution:

Given that,

a ) n = 10

= 64% =0.64

1 - = 1 - 0.64 = 0.36

=   = 0.07

= ( 1 - ) / n

=   0.64 * 0.36 / 10

= 0.1518

= 0.1518

P(   > 0.79 )

= 1 - P (   < 0.79 )

= 1 - P ( -    / ) < ( 0.79 - 0.64 / 0.1518 )

= 1 - P ( z < 0.15 / 0.1518 )

= 1 - P ( z < 0.99 )

Using z table

= 1 - 0.8389

=0.1611

Probability = 0.1611

b ) n = 42

= 64% =0.64

1 - = 1 - 0.64 = 0.36

=   = 0.07

= ( 1 - ) / n

=   0.64 * 0.36 / 42

= 0.0741

= 0.0741

P(   > 0.79 )

= 1 - P (   < 0.79 )

= 1 - P ( -    / ) < ( 0.79 - 0.64 / 0.0741 )

= 1 - P ( z < 0.15 / 0.0741 )

= 1 - P ( z < 2.02 )

Using z table

= 1 - 0.9783

= 0.0217

Probability = 0.0217