Answer: N(20, 4) distribution.
Step-by-step explanation:
Normal approximation to Binomial :
The normal approximation is used for binomial distribution having parameters n and p as
[tex]\mu=np\\\\ \sigma=\sqrt{np(1-p)}[/tex]
if x is the random variable then x has [tex]N(\mu, \sigma)[/tex].
Given : As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local supermarket.
The probability that a shopper will buy a packet of crackers after tasting the free sample : p=0.20.
Different shoppers can be regarded as independent trials.
if X is the number among the next 100 shoppers who buy a packet of crackers after tasting a free sample.
Then, Mean and standard deviation for x will be :
[tex]\mu=(100)(0.20)=20\\\\ \sigma=\sqrt{20(1-0.20)}=\sqrt{16}=4[/tex]
i.e. X has approximately an N(20, 4) distribution.
