SOLUTION: According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 145 people in Uganda. Let X = the number of people

(a)  It is a binomial distribution with n= 145 trials and the probability of success p= 0.09 
     for each individual trial.

     I do not understand the meaning of these hieroglyphs under (a), so you should determine it on your own.



(b)  The mean for this binomial distribution is  m = n*p = 0.09*145 = 13.05.

     The standard deviation is  SD =  =  = 3.446084735.


Questions (c), (d) and (e) assume that you will use normal distribution formulas for this binomial distribution 
as an approximation.  Statistically, it is possible because the number of trials n= 145 is great.



(c)  Use your regular calculator TI-83/84 with standard function normcdf 
     (which stands for Cumulative Distribution Function).

     For (c), the probability is the area under the normal curve (with the mean and standard deviation determined in (a))
     in the interval (14.5,15.5).  This interval "with plus/minus halves" is the continuous correction, when we use normal
     distribution as an approximation to binomial.  So, we write

                       z1     z2    mean     SD           <<<---===  formatting pattern
         P = normcdf( 14.5,  15.5, 13.05, 3.446084735).


     Alternatively, you may use free of charge online calculator for normal distribution
         https://onlinestatbook.com/2/calculators/normal_dist.html

     To be honest, I always use it in my calculations, since it has simple and very convenient interface
     and great visual output.

     You can be restricted in using calculators, so use whichever is an appropriate for you.

     In any case, the answer for  (c)  is  P = 0.0984.



(d)  For (d), the probability is the area under the normal curve (with the mean and standard deviation determined in (a))
     in the interval (,).  This interval is the continuous correction to "at most 10", when we use normal
     distribution as an approximation to binomial.  So, we write

                        z1     z2    mean     SD           <<<---===  formatting pattern
         P = normcdf( -9999,  10.5, 13.05, 3.446084735).


     Again, alternatively, you may use free of charge online calculator for normal distribution
         https://onlinestatbook.com/2/calculators/normal_dist.html


     In any case, the answer for  (d)  is  P = 0.2297.



(e)  For (e), the probability is the area under the normal curve (with the mean and standard deviation determined in (a))
     in the interval (,).  This interval is the continuous correction to "more than 25", when we use normal
     distribution as an approximation to binomial.  So, we write

                       z1     z2    mean     SD           <<<---===  formatting pattern
         P = normcdf( 25.5,  9999, 13.05, 3.446084735).


     Again, alternatively, you may use free of charge online calculator for normal distribution
         https://onlinestatbook.com/2/calculators/normal_dist.html


     In any case, the answer for  (e)  is  P = 0.0002.

     It is a vanishing value; when the value of probability is vanishing, normal approximation works badly 
     (consider it as my warning to you).