Question

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 is 0.200. 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 X has approximately an
N(20, 4) distribution.
N(20, 16) distribution.
N(0.2, 16) distributio

Answer 1

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

$\mu=np\\\\ \sigma=\sqrt{np(1-p)}$

if x is the random variable then x has $N(\mu, \sigma)$.

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 :

$\mu=(100)(0.20)=20\\\\ \sigma=\sqrt{20(1-0.20)}=\sqrt{16}=4$

i.e. X has approximately an  N(20, 4) distribution.