SOLUTION: Of the population of customers of a store, a proportion of 0.4 are not satisfied with the service offered by the store. In a random sample of 400 customers, what is the probabili

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Question 1185104: Of the population of customers of a store, a proportion of 0.4 are not
satisfied with the service offered by the store. In a random sample of 400
customers, what is the probability that between 156 and 240 customers will be
satisfied with the service offered by the store?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Of the population of customers of a store, a proportion of 0.4 are not
satisfied with the service offered by the store. In a random sample of 400
customers, what is the probability that between 156 and 240 customers will
be satisfied with the service offered by the store?

The word "between" is ambiguous as to whether is means "inclusive" or
exclusive.

Does "between 156 and 240" mean to include 156 and 240, or exclude them?
I'll assume it means to include them.

This is a binomial experiment, but we must use the normal approximation.
The binomial feature on the calculator is not accurate for large n.

n = 400
p = 0.4
μ = np = (400)(0.4) = 160
σ = √(npq) = √[(400)(0.4)(0.6)] = 9.797958971

So we want P(155.5 < X < 240.5)

On your TI-84, press ON CLEAR 2ND VARS 2

Make the screen read like this:

     normalcdf
lower:155.5
upper:240.5
μ:160
σ:9.797958971     
Paste

Use the down arrow key to highlight Paste
Press ENTER

See this:

normalcdf(155.5,240.5,160,9.797958971)

Press ENTER
 
Read 0.6769831887

Round to 0.6770

Edwin