Question

A manufacturer ships toasters in cartons of 25. In each​ carton, they estimate a 4​% chance that one of the toasters will need to be sent back for minor repairs. In a batch of 12,500 ​toasters, what are the chances that fewer than 475 need to be​ returned?

Answer 1

here,n=12500

p=0.04

binomial distribution

check the condition for normal approximation,

np=12500*0.04=500

n(1-p) =12500*0.96 = 12000

both are greater than 10 ,so, binomial distribution can be approximated to normal distribution

now

Sample size , n =    12500
Probability of an event of interest, p =   0.04
left tailed  
X < 475

Mean = np =    500
std dev ,σ=√np(1-p)=   21.9089023

Z =   (X - µ ) / σ =   -1.14          
                  
P(X ≤   475   ) = P(Z ≤   -1.14   ) =   0.1269(answer) [ excel formula =normsdist(z) ]
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