Question

A movie theater chain has lost business during a global health crisis. They are surveying a SRS of 70 customers

each month to understand what would make their customers feel safe enough to return. Suppose that in July,

87% of customers wanted to order tickets digitally, and in August, 90% of customers wanted order tickets

digitally.

They wonder whether the demand for digital tickets is changing, so they look at the difference in the sample

proportions (PA - P3)

What will be the shape of the sampling distribution of PA Ps, and why?

Answer 1

Answer: D

Not normal, because we expect fewer than 10 customers who do not want to order tickets digitally in both samples.

Explanation: Khan Answer

10% of customers in July would not want to order tickets digitally because 90% do. In an SRS of 70 customers, that means only 7 would not want to order tickets digitally. 13% of customers in August would not want to order tickets digitally because 87% do. In an SRS of 70 customers, that means only 9.1 would not want to order tickets digitally. Because both of these counts are less than 10, we can not assume normality.

Answer 2

The shape of the sampling distribution of the proportions is; Not normal because np < 10 in both samples and as such we expect less than 10 customers that do not want to order tickets digitally in both cases.

Normal Distribution

We are told that they are surveying a Specific Random Sample (SRS) of 70 customers. Thus; n = 70

Now, In July, 87% of customers wanted to order tickets digitally.

Thus, proportion that didn't want to order tickets digitally in July is; p = 13%

In July, number of people out of the SRS of 70 that didn't want to order tickets digitally is;

np = 70 × 13% = 9.1

Now,in August, 90% of customers wanted to order tickets digitally.

Thus, proportion that didn't want to order tickets digitally in August is; p = 10%

In August, the number of people out of the SRS of 70 that didn't want to order tickets digitally is;

np = 70 × 10% = 7

For both months of July and August, we see that np < 10 and one of the requirements for the sampling distribution to be normal is that np has to be greater than 10.

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