The (population) proportion of students who use the internet as their major reso

Question

The (population) proportion of students who use the internet as their major resource for a school project in the past year is 0.72. Suppose that you take a sample of n = 500 students, and record the number of students who used the internet as a major resource for their school project during the past year. Let p be the proportion of the 500 students who used the internet as a major resource in the past year.

A. Can you use the normal approximation to approximate the distribution of p ?

B. What is the probability that the sample proportion lies between 0.68 and 0.72?

Explanation / Answer

A)

Here, n = 500, p = 0.72.

Hence, YES, we can use the normal approximation as

n p (1 - p) = 500*0.72*(1-0.72) = 100.8 > 5.

**********************

b)

Here,          
n =    500      
p =    0.72      
We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    0.68      
x2 = upper bound =    0.72      
u = mean = p =    0.72      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.020079841      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.992047682      
z2 = upper z score = (x2 - u) / s =    0      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.023182913      
P(z < z2) =    0.5      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.476817087   [ANSWER]  

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