In: Statistics and Probability
74% of freshmen entering public high schools in 2006 graduated with their class in 2010. A random sample of 81 freshmen is selected. Find the probability that the proportion of students who graduated is greater than 0.750 . Write only a number as your answer. Round to 4 decimal places (for example 0.1048). Do not write as a percentage.
Solution
Given that,
p = 0.74
1 - p = 1-0.74=0.26
n = 81
= p =0.74
= [p( 1 - p ) / n] = [(0.74*0.26) /81 ] = 0.0487
P( >0.750 ) = 1 - P( < )
= 1 - P(( - ) / < (0.750 -0.74) / 0.0487)
= 1 - P(z < 0.21)
Using z table
= 1 -0.5832
=0.4168
probability=0.4168