Question

Problem 2

In a survey, 1,000 people were asked if they shop at the X store regularly; the possible answers were dichotomous because they could only answer Yes or No. The results showed that 30% of the respondents answered yes (that is, they do buy at the store X regularly). If, based on this information, an experiment is conducted where 100 of these people are randomly selected, and these people are asked if they shop at the X store regularly, what is the probability that 20% or less of these 100 people interviewed answer Yes?

________________________                    =                             ____________________________%

You have to include the Excel formulas used.

Answer 1

We can consider this experiment as a binomial distribution where

Let 'X' be the variable denoting people who answered yes.

We have been given that out of 1000, 30% answered yes.

Therefore our probability of success (p) = 0.3  

We have sample of 100 that means n = 100 trials

We need to find the probability that 20% or less answered yes, that means 20 (100*0.2) or less people answered yes.

.............It's cumulative

Using excel we can get the exact value by using the function 'binomdist(20,100,0.30,true)'.

The last argument 'true' is for cumulative.

We can do this by using normal approximation since

1. np > 5
2. n > 30 ....(n is large)

But since we are approximating a discrete distribution to a continuos we need to do continuity correction.

= P( X < 20.5)

=

= P( N(0,1) < -2.07)

= 1 - P( N(0,1) < 2.07)

= 1 - 0.9809........................Using normal dist tables or excel function 'normsdist(2.07)'

= = 1.91%