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 the crackers after tasting a free sample, then the probability that fewer than 30 buy a packet after tasting a free sample is ______ .

Answer 1

Answer: Our required probability is 0.99338.

Step-by-step explanation:

Since we have given that

n = 100

p = 0.200

So, $np=100\times 0.2=20>5$

So, we can apply normal approximation.

Mean = 20

Standard deviation = $\sqrt{npq}=\sqrt{100\times 0.2\times 0.8}=\sqrt{16}=4=\sigma$

Since $z=\dfrac{\bar{X}-\mu}{\sigma}$

So, Probability that fewer than 30 but a packet after testing a free sample is given by

$P(X<30)\\\\=P(z<\dfrac{30-20}{4})\\\\=P(z<\dfrac{10}{4})\\\\=P(z<2.5)\\\\=0.9938$

Hence, our required probability is 0.99338.