4. As part of a promotion for a new type of cracker, free 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 0.3. Different shoppers can be regarded as independent trials. Let p be the proportion of the next 60 shoppers that buy a packet of the crackers after tasting a free sample. a) What are the mean and standard deviation of the distribution of the sample proportion

For this case we need to check the conditions in order to use the normal approximation:

1)

2)

Since both conditions are satisfied and the independence condition is assumed we can use the normal approximation given by:

The mean would be given by:

And the deviation is given by:

Step-by-step explanation:

For this case we know the following info:

n =60 represent the sample size

represent the estimated proportion of people that will buy a packet of crackers after tasting

For this case we need to check the conditions in order to use the normal approximation:

1)

2)

Since both conditions are satisfied and the independence condition is assumed we can use the normal approximation given by:

The mean would be given by:

And the deviation is given by:

a. she will receive a refund of $278.

step-by-step explanation: