One method for estimating the availability of office space in large cities is to conduct a random sample of offices, and calculate the proportion of offices currently being used. Suppose that real estate agents believe that p = 0.70 of all offices are currently occupied, and decide to take a sample to assess their belief. They are considering a sample size of n = 40.
a)Show that this sample size is large enough to justify using the normal approximation to the sampling distribution of 
.
b)What is the mean of the sampling distribution of 
if the real estate agents are correct?
c)What is the standard deviation of the sampling distribution of 
if the real estate agents are correct?
d)If the real estate agents are correct, what is the probability that a sample proportion, 
, would differ from p = 0.70 by as much as 0.05?
Definitions:
Drosophila Melanogaster
Drosophila Melanogaster, commonly known as the fruit fly, is a widely used model organism in genetics, developmental biology, and related fields.
Photosynthetic Organisms
Living entities that can convert light energy, usually from the sun, into chemical energy through the process of photosynthesis.
Primary Endosymbiosis
A symbiotic relationship in which a eukaryotic cell engulfs a prokaryote, leading to the evolution of important cell organelles, such as mitochondria and chloroplasts.
Secondary Endosymbiosis
An evolutionary process by which a eukaryotic cell engulfs another eukaryotic cell, leading to a symbiotic relationship.
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