Question

The magazine Sports Illustrated asked a random sample of 750 Division 1

college athletes, "Do you believe performance-enhancing drugs are a
problem in college sports?" Suppose that 30% of all Division I athletes
think that these drugs are a problem. Let p be the sample proportion who
say that these drugs are a problem. The sampling distribution of p is
approximately Normal because
There are least 7570 Division I college athletes
np = 225 and n(1-P) = 525
a large sample size like n = 750 guarantees it
the sampling distribution of p always has this shape
a random sample was chosen

Answer 1

np=225 and n(1-p)=525 are both at least 10.

Answer 2

np = 225 and n(1 - p) = 525 are both atleast 10

Step-by-step explanation:

The sampling distribution of a sample proportion is approximately normal if :

np and n(1 - p) are both ≥ 10

The sample size, n = 750

The proportion, p = 0.30

np = (750 * 0.30) = 225

n(1 - p) = (750 * (1 - 0.30)) = (750 * 0.70) = 525

Hence, the sampling distribution of p is approximately normal because ; np and n(1 - p) are ≥ 10