Question

High school graduates: Approximately 78% of freshmen entering public high schools in the United States in 2005 graduated with their class in 2009. A random sample of 128 freshmen is chosen.

(a)Find the mean μp

.(b)Find the standard deviation σp

.

(c)Find the probability that less than 91% of freshmen in the sample graduated.

(d)Find the probability that between 68%and 83% of freshmen in the sample graduated.

(e)Find the probability that more than 68%of freshmen in the sample graduated.Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

Answer 1

Solution :

Given that ,

p = 0.78

1 - p = 0.22

n = 128

a)

= p = 0.78  

b)

= (p*(1-p))/n =  (0.78*0.22)/ 128= 0.03661

c)

P( < 0.91 ) = P(( - ) / < (0.91 - 0.78) / 0.03661)

= P(z < 3.55)

= 0.9998

Probability = 0.9998

d)

P(0.68 < <0.83 ) = P((0.68-0.78)/0.03661 ) < ( - ) /  < (0.83-0.78) /0.03661 ) )

= P(-2.73 < z < 1.37)

= P(z < 1.37) - P(z < -2.73)

= 0.9147 - 0.0032

= 0.9115

Probability = 0.9115

e)

P( > 0.68) = 1 - P( < 0.68)

= 1 - P(( - ) / < (0.68-0.78) /0.03661 )

= 1 - P(z < -2.73)

= 1 - 0.0032

= 0.9968

Probability = 0.9968