Question

According to a 2009 Reader's Digest article, people throw away approximately 13% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 210 grocery shoppers to investigate their behavior. What is the probability that the sample proportion is between 0.05 and 0.16? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer 1

the distribution of sample proportion would be obtained here as:

The probability here is computed as:
P( 0.05 < p < 0.16)

Converting it into a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.9020 is the required probability here.