Question

A company sells meal kits. Suppose that 70% of the first-time customers who order a vegetarian meal will order

again, while 65% of the first-time customers who order a gluten-free meal will order again. The company takes
separate random samples of 50 first-time customers who order each kind of meal. The company will then look at
the difference (vegetarian – gluten free) between the proportions of customers who order again in each
sample.
What will be the shape of the sampling distribution of the difference in sample proportions, and why?

Answer 1

Approximately normal, because we expect 35 successes and 15 failures from vegetarian orders, and 32.5 and 17.5 from gluten-free orders, and all of these counts are at least 10

Explanation:

Answer 2

Answer: A

Approximately normal, because we expect 35 successes and 15 failures from vegetarian orders, and 32.5 and 17.5 from gluten-free orders, and all of these counts are at least 10

Step-by-step explanation: Khan Answer

For vegetarian orders 70% order again, so with a sample size of 50 we will have an estimated 35 people order again:
`.7*50=35,50-35=15` This results in 35 successes and 15 failures. For gluten-free orders 65% order again, so with a sample size of 50 we will have an estimated 32.5 people order again:
`.65*50=32.5,50-32.5=17.5` This results in 32.5 successes and 15 failures. Because these are all greater than 10, we can assume normality.