A scientist claims that 7% 7 % of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 600 600 viruses would differ from the population proportion by greater than 3% 3 % ? Round your answer to four decimal places.

The probability is

Step-by-step explanation:

From the question we are told that

   The population proportion is

   The mean of the sampling distribution is  

   The sample size is n = 600

Generally the standard deviation is mathematically represented as

=>        

=>        

Generally the probability that the proportion of airborne viruses in a sample of 600 viruses would differ from the population proportion by greater than 3% is mathematically represented as

=>  

Now  add p  to  both side of the inequality

=>  

=>  

Now  converting the probabilities to their respective standardized score

=>

=>

=>  

From the z-table  

and

So

=>  

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)