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.

Explanation:

Normal approximation to Binomial :

The normal approximation is used for binomial distribution having parameters n and p as

`\mu=np\\\\ \sigma=√(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=√(20(1-0.20))=√(16)=4`

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