it has been reported that 80% of federal government employees use e-mail. if a s

Question

it has been reported that 80% of federal government employees use e-mail. if a sample of 200 federal government employees is selected, find the mean, variance and standard deviation of the number who use e-mail. find the probability that less than 150 employees use email. please explain steps! thank you. it has been reported that 80% of federal government employees use e-mail. if a sample of 200 federal government employees is selected, find the mean, variance and standard deviation of the number who use e-mail. find the probability that less than 150 employees use email. please explain steps! thank you. it has been reported that 80% of federal government employees use e-mail. if a sample of 200 federal government employees is selected, find the mean, variance and standard deviation of the number who use e-mail. find the probability that less than 150 employees use email. please explain steps! thank you.

Explanation / Answer

Here,

n = 200,

p = 0.8

So

u = mean = np =    160   [ANSWER]

variance = np(1-p) = 32 [ANSWER]  
          
s = standard deviation = sqrt(np(1-p)) =    5.656854249   [ANSWER]

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

We first get the z score for the critical value:          
          
x = critical value =    149.5      
u = mean = np =    160      
          
s = standard deviation = sqrt(np(1-p)) =    5.656854249      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -1.856155301      
          
Thus, the left tailed area is          
          
P(z <   -1.856155301   ) =    0.031715713 [ANSWER]

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