Question

Eight percent of customers of a bank keep a minimum balance of $500 in their checking accounts. What is the probability that in a random sample of 100 customers, 10 or fewer keep the minimum balance of $500? (Hint: Normal approximation to binomial distribution is required)

6b) ​Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years, (based on data from “Getting Things Fixed,” Consumer Reports).

​If you want to provide a warranty so that only 3% of the TV sets will be replaced before the warranty expires, the length of warranty you would recommend would be how many years.?

Answer 1

a)

Sample size , n =    100          
Probability of an event of interest, p =   0.8          
left tailed              
X ≤    10          
              
Mean = np =    80          
std dev ,σ=√np(1-p)=   4.0000          
              
P(X ≤   10   ) = P(Xnormal ≤   10.5   )
              
Z=(Xnormal - µ ) / σ =    (10.5-80)/4)=       -17.375  
              
=P(Z≤   -17.375   ) =    0.0000000 (answer)
==============

b)

µ=   8.2  
σ =    1.1  
P(X≤x) =   0.03  
      
z value at 0.03=   -1.8808   (excel formula =NORMSINV(0.03))
z=(x-µ)/σ      
so, X=zσ+µ=   -1.881   *1.1+8.2
X =   6.13 (answer)

please revert for doubts and

please UPVOTE the solution