Question

according to a 2017 Pew survey, 60% of Americans aged 18-29 say the primary way they watch TV is with streaming services. Suppose a random sample of 200 Americans from this age group is selected.

1. How many people in this sample would we expect to watch TV via a streaming service?

2. Verify that the conditions for the central limit theorem have been met. State each condition as part of your verification.

3. Find the standard error for this sample.

4. Would it be surprising to find that 125 people in the sample stream their TV shows? Why or why not?

Answer 1

1. Here given is

n = 200, p = 0.60

expect number of people to watch TV via a streaming service = np = 200 * 0.60 = 120

2. For central limit condition to follow,

np > 5 and nq > 5

here both conditions are fulfilled so central limit theorm will follow.

3. standard error = sqrt [p*(1-p) *n] = sqrt [0.60 * 0.40 * 200] = 6.93

4. Here

P(n > 125)

Z = (125 - 120)/6.93= 0.722

P(n > 125) = 1 - P(Z < 0.722) = 1 - 0.7648 = 0.2352

no we would not be surprise that more than 125 people  in the sample stream their TV shows as the probability of that event is not unusual or rare to happen.